{"id":48415,"date":"2024-02-19T18:09:33","date_gmt":"2024-02-19T10:09:33","guid":{"rendered":"https:\/\/swarma.org\/?p=48415"},"modified":"2024-02-19T18:09:33","modified_gmt":"2024-02-19T10:09:33","slug":"nat-rev-phys-%e9%87%8d%e7%a3%85%e7%bb%bc%e8%bf%b0%ef%bc%9a%e5%a4%8d%e6%9d%82%e7%bd%91%e7%bb%9c%e7%9a%84%e9%b2%81%e6%a3%92%e6%80%a7%e5%92%8c%e9%9f%a7%e6%80%a7","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=48415","title":{"rendered":"Nat. Rev. Phys.\u91cd\u78c5\u7efc\u8ff0\uff1a\u590d\u6742\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u548c\u97e7\u6027"},"content":{"rendered":"
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Oriol Artime\uff0cMarco Grassia\uff0cManlio De Domenico\uff0cJames P. Gleeson\u7b49<\/span><\/span> | \u4f5c\u8005<\/span><\/strong><\/section>\n
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1. \u7f51\u7edc\u74e6\u89e3\u95ee\u9898\u7684\u8d77\u6e90\u4e0e\u53d1\u5c55\uff1a\u4ece\u7f51\u7edc\u9c81\u68d2\u6027\u5230\u7f51\u7edc\u74e6\u89e3\u95ee\u9898<\/strong><\/span><\/section>\n
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2. \u590d\u6742\u7f51\u7edc\u7ea7\u8054\u5931\u6548\u7684\u52a8\u529b\u5b66\uff1a\u7ea7\u8054\u5931\u6548\u6a21\u578b\u4e0e\u9632\u6b62\u5d29\u6e83\u65b9\u6cd5<\/strong><\/section>\n

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3. \u7f51\u7edc\u74e6\u89e3\u95ee\u9898\u7684\u672a\u6765\uff1a\u4ece\u7ed3\u6784\u6027\u74e6\u89e3\u5230\u529f\u80fd\u6027\u74e6\u89e3<\/strong><\/section>\n
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Robustness and resilience of complex networks<\/span><\/section>\n
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    \u5728\u751f\u7269\u5b66\u3001\u793e\u4f1a\u5b66\u548c\u5de5\u7a0b\u5b66\u7b49\u9886\u57df\uff0c\u590d\u6742\u7cfb\u7edf\u53ef\u4ee5\u901a\u8fc7\u4ea4\u4e92\u7f51\u7edc\u4e2d\u5355\u5143\u95f4\u7684\u4fe1\u606f\u4ea4\u6362\u6765\u5b9a\u4e49\uff0c\u5c55\u73b0\u51fa\u5982\u5f02\u8d28\u6027\u3001\u6a21\u5757\u5316\u548c\u5c42\u7ea7\u7b49\u591a\u6837\u7684\u7ed3\u6784\u6a21\u5f0f\u3002<\/span><\/p>\n<\/li>\n

  • \n

    \u7531\u4e8e\u590d\u6742\u7f51\u7edc\u7684\u76f8\u4e92\u8fde\u63a5\u7279\u6027\uff0c\u5b83\u4eec\u80fd\u591f\u5c06\u5fae\u5c0f\u7684\u5e72\u6270\u653e\u5927\u81f3\u6574\u4e2a\u7cfb\u7edf\u5c42\u9762\uff0c\u56e0\u6b64\u7406\u89e3\u5b83\u4eec\u5728\u9762\u5bf9\u5916\u90e8\u6270\u52a8\u548c\u5185\u90e8\u6545\u969c\u65f6\u7684\u9c81\u68d2\u6027\u81f3\u5173\u91cd\u8981\u3002<\/span><\/p>\n<\/li>\n

  • \n

    \u7814\u7a76\u590d\u6742\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u548c\u97e7\u6027\u6d89\u53ca\u63a2\u8ba8\u901a\u5e38\u4f9d\u8d56\u4e8e\u5ea6\u503c\u8fde\u901a\u6027\u3001\u7a7a\u95f4\u5d4c\u5165\u3001\u76f8\u4e92\u4f9d\u8d56\u548c\u8026\u5408\u52a8\u529b\u5b66\u7b49\u7279\u5f81\u7684\u76f8\u53d8\u73b0\u8c61\u3002<\/span><\/p>\n<\/li>\n

  • \n

    \u7f51\u7edc\u79d1\u5b66\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u7406\u8bba\u548c\u8ba1\u7b97\u65b9\u6cd5\u6765\u91cf\u5316\u7cfb\u7edf\u5bf9\u6270\u52a8\u7684\u9c81\u68d2\u6027\uff0c\u5e76\u63d0\u4f9b\u4e86\u57fa\u7840\u65b9\u6cd5\u6765\u8bbe\u8ba1\u9c81\u68d2\u6027\u3001\u8bc6\u522b\u65e9\u671f\u9884\u8b66\u4fe1\u53f7\u548c\u5236\u5b9a\u9002\u5e94\u6027\u54cd\u5e94\u3002<\/span><\/p>\n<\/li>\n

  • \n
    \u8fd9\u4e9b\u65b9\u6cd5\u5728\u7cfb\u7edf\u751f\u7269\u5b66\u3001\u7cfb\u7edf\u795e\u7ecf\u79d1\u5b66\u3001\u5de5\u7a0b\u5b66\u4ee5\u53ca\u793e\u4f1a\u548c\u884c\u4e3a\u79d1\u5b66\u7b49\u591a\u4e2a\u5b66\u79d1\u4e2d\u90fd\u6709\u5e94\u7528\u3002<\/span><\/section>\n<\/li>\n<\/ul>\n

    <\/section>\n

    <\/section>\n

    \n
    \n
    \n
    \n
    \n

    <\/section>\n

    <\/section>\n
    \n
    <\/svg><\/section>\n<\/section>\n<\/section>\n
    \n

    \u4e00\u3001\u5f15\u8a00 <\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


    <\/p>\n

    \u5728\u751f\u7269\u5b66\u3001\u793e\u4f1a\u5b66\u3001\u793e\u4f1a\u751f\u6001\u5b66\u548c\u5de5\u7a0b\u5b66\u7b49\u5e7f\u6cdb\u9886\u57df\u4e2d\uff0c\u65e0\u8bba\u662f\u86cb\u767d\u8d28\u3001\u795e\u7ecf\u5143\u3001\u4e2a\u4f53\u8fd8\u662f\u7269\u79cd\u7b49\u5355\u4f4d\uff0c\u90fd\u901a\u8fc7\u590d\u6742\u7684\u4ea4\u4e92\u7f51\u7edc\u8fdb\u884c\u4fe1\u606f\u4ea4\u6362[1-3]\u3002\u8fd9\u4e9b\u7f51\u7edc\u6240\u4ea7\u751f\u7684\u8fde\u63a5\u6a21\u5f0f\u901a\u5e38\u5177\u6709\u5f02\u8d28\u6027\u548c\u91cd\u5c3e\u7279\u5f81\uff0c\u5176\u4e2d\u5c11\u6570\u5355\u5143\u4f5c\u4e3a\u67a2\u7ebd\uff0c\u800c\u591a\u6570\u5176\u4ed6\u5355\u5143\u8fde\u63a5\u8f83\u5c11[4-8]\u3002\u8fd9\u4e9b\u7279\u5f81\u663e\u73b0\u51fa\u660e\u663e\u7684\u4ecb\u89c2<\/span>\uff08mesoscale\uff09<\/span>\u7ec4\u7ec7\u7ed3\u6784\uff0c\u5305\u62ec\u6a21\u5757\u5316[9-13]\u3001\u5c42\u7ea7\u7ed3\u6784[14-16]\u3001\u7f51\u7edc\u7684\u7f51\u7edc<\/span>\uff08Networks of networks\uff09<\/span> [17-22]\u3001\u9ad8\u9636\u7ed3\u6784[23-25]\u4ee5\u53ca\u9690\u542b\u7684\u51e0\u4f55\u5f62\u6001[26-28]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u9274\u4e8e\u590d\u6742\u7f51\u7edc\u5728\u81ea\u7136\u548c\u4eba\u5de5\u7cfb\u7edf\u4e2d\u65e0\u5904\u4e0d\u5728\uff0c\u7406\u89e3\u5b83\u4eec\u5728\u4f55\u79cd\u6761\u4ef6\u4e0b\u80fd\u591f\u5145\u5206\u53d1\u6325\u529f\u80fd\uff0c\u4ee5\u53ca\u5b83\u4eec\u5728\u5e94\u5bf9\u5916\u90e8\u6270\u52a8\u548c\/\u6216\u5185\u90e8\u6545\u969c\u7684\u8106\u5f31\u6027\u7a0b\u5ea6\uff0c\u663e\u5f97\u81f3\u5173\u91cd\u8981[29]\u3002\u5b9e\u9645\u4e0a\uff0c\u590d\u6742\u7f51\u7edc\u7684\u4e92\u8fde\u6027\u8d28\u9762\u5bf9\u5e72\u6270\u53ef\u80fd\u4ea7\u751f\u6b63\u9762\u6216\u8d1f\u9762\u5f71\u54cd\u3002\u590d\u6742\u7f51\u7edc\u80fd\u591f\u5c55\u73b0\u51fa\u4e30\u5bcc\u7684\u884c\u4e3a\uff0c\u4ece\u7b80\u5355\u5730\u627f\u53d7\u5e76\u6d88\u5316\u7279\u5b9a\u7c7b\u578b\u7684\u5c0f\u5e45\u6270\u52a8\u800c\u4e0d\u5f15\u8d77\u5927\u5c3a\u5ea6\u5f71\u54cd\uff0c\u5230\u653e\u5927\u5fae\u5c0f\u7684\u521d\u59cb\u635f\u5bb3\u76f4\u81f3\u6269\u5c55\u81f3\u5f71\u54cd\u6574\u4e2a\u7cfb\u7edf\u3002\u4e00\u4e2a\u5178\u578b\u7684\u4f8b\u5b50\u662f\uff0c\u4f4d\u4e8e\u7cfb\u7edf\u5355\u5143\u95f4\u4fe1\u606f\u4ea4\u6362\u5173\u952e\u8282\u70b9\u7684\u5c40\u90e8\u6270\u52a8<\/span>\uff08\u5982\u4fe1\u53f7\u4f20\u9012\u3001\u7535\u529b\u91cd\u65b0\u5206\u914d\u7b49\uff09<\/span>\u89e6\u53d1\u7684\u7ea7\u8054\u5931\u6548[30,31]\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u590d\u6742\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u548c\u97e7\u6027\u7279\u5f81\u8868\u73b0\u4e3a\u4e0d\u540c\u7c7b\u578b\u7684\u76f8\u53d8\u73b0\u8c61[32,33]\u3002\u8fd9\u4e9b\u76f8\u53d8\u7684\u6027\u8d28\u53d6\u51b3\u4e8e\u7cfb\u7edf\u7684\u7ed3\u6784\u7279\u5f81<\/span>\uff08\u4f8b\u5982\u5b83\u662f\u5426\u7a7a\u95f4\u5d4c\u5165\u3001\u662f\u5426\u4e0e\u5176\u4ed6\u7cfb\u7edf\u76f8\u4e92\u4f9d\u8d56\u6216\u662f\u591a\u5c42\u6b21\u7684[34-36]\uff09<\/span>\u548c\u5176\u52a8\u529b\u5b66\u7279\u6027<\/span>\uff08\u5982\u5b58\u5728\u96c6\u4f53\u884c\u4e3a\u7684\u6d8c\u73b0\u60c5\u51b5\uff0c\u4f8b\u5982\u540c\u6b65\u3001\u6d41\u884c\u75c5\u4f20\u64ad\u6216\u8026\u5408\u52a8\u529b\u5b66\u7b49[37-40]\uff09<\/span>\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u7814\u7a76\u7cfb\u7edf\u5728\u7ed3\u6784\u548c\u52a8\u529b\u5b66\u7a33\u5b9a\u4e0b\u5bf9\u6270\u52a8\u7684\u54cd\u5e94\u81f3\u5173\u91cd\u8981\uff0c\u8fd9\u7c7b\u7814\u7a76\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u9884\u6d4b\u7cfb\u7edf\u53ef\u80fd\u53d1\u751f\u7684\u4e34\u754c\u76f8\u53d8[41]\u3002\u4f8b\u5982\uff0c\u7406\u89e3\u7ec6\u80de\u4ee3\u8c22\u7f51\u7edc\u5728\u7279\u5b9a\u9176\u53cd\u5e94\u7684\u6fc0\u6d3b\u6216\u6291\u5236\u4e0b\u7684\u7ea7\u8054\u5931\u6548\u548c\u9c81\u68d2\u6027\uff0c\u5bf9\u4e8e\u5f00\u53d1\u7279\u5b9a\u7597\u6cd5\u3001\u836f\u7269\u518d\u5229\u7528\uff0c\u4e43\u81f3\u4e8e\u7f51\u7edc\u548c\u7cfb\u7edf\u533b\u5b66\u9886\u57df\u7684\u5e7f\u6cdb\u5e94\u7528\u90fd\u6709\u91cd\u8981\u610f\u4e49[9,42,43]\u3002\u7c7b\u4f3c\u5730\uff0c\u86cb\u767d\u8d28-\u86cb\u767d\u8d28\u76f8\u4e92\u4f5c\u7528\u7f51\u7edc\u5bf9\u5185\u90e8\u9519\u8bef\u6216\u5916\u90e8\u5e72\u6270\u7684\u9c81\u68d2\u6027\uff0c\u76f4\u63a5\u5173\u8054\u5230\u7ec6\u80de\u529f\u80fd\u53ca\u5176\u5728\u751f\u547d\u6811\u4e2d\u7684\u97e7\u6027[44]\u3002\u5728\u4eba\u8111\u4e2d\uff0c\u5c40\u90e8\u6270\u52a8\u53ef\u80fd\u4e0e\u4e2d\u98ce[45,46]\u7b49\u75c5\u7406\u72b6\u51b5\u6709\u5173\u3002\u751f\u6001\u548c\u793e\u4f1a\u751f\u6001\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u53ca\u6062\u590d\u80fd\u529b[47-51]\uff0c\u4f9d\u8d56\u4e8e\u5b83\u4eec\u5bf9\u6270\u52a8\u7684\u9c81\u68d2\u6027\u3002\u5728\u793e\u4f1a\u7cfb\u7edf\u4e2d\uff0c\u63a7\u5236\u6d41\u884c\u75c5\u7206\u53d1\u4e0e\u57fa\u7840\u793e\u4ea4\u7f51\u7edc\u7684\u6e17\u6d41\u7279\u6027[38]\u7d27\u5bc6\u76f8\u5173\uff0c\u800c\u91d1\u878d\u548c\u7ecf\u6d4e\u7cfb\u7edf\u4e2d\u7cfb\u7edf\u6027\u98ce\u9669\u7684\u4f20\u64ad[53-56]\uff0c\u4f9d\u8d56\u4e8e\u5b83\u4eec\u5bf9\u7ea7\u8054\u5931\u6548\u7684\u97e7\u6027\uff0c\u8fd9\u4e0e\u7535\u7f51\u4e2d\u5bfc\u81f4\u666e\u904d\u505c\u7535\u7684\u60c5\u51b5[57,58]\u7c7b\u4f3c\u3002\u4ece\u4e92\u8054\u7f51[61,62]\u5230\u822a\u7a7a\u8def\u7ebf[63]\u7b49\u4ea4\u901a\u7f51\u7edc\u7684\u6548\u7387\uff0c\u4ee5\u53ca\u5b83\u4eec\u5bf9\u9519\u8bef\u548c\u6270\u52a8\u7684\u5bb9\u5fcd\u5ea6\uff0c\u90fd\u53ef\u4ee5\u901a\u8fc7\u6e17\u6d41\u5206\u6790\u6765\u7406\u89e3[59,60]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5c3d\u7ba1\u8fd9\u4e9b\u5e94\u7528\u65e0\u5904\u4e0d\u5728\uff0c\u4e14\u7406\u89e3\u5bfc\u81f4\u7cfb\u7edf\u5d29\u6e83\u7684\u6761\u4ef6\u81f3\u5173\u91cd\u8981\uff0c\u4f46\u5bf9\u76f8\u5173\u6587\u732e\u7684\u7cfb\u7edf\u6027\u6982\u8ff0\u4ecd\u7136\u7f3a\u5931\u3002\u8fd9\u7bc7\u6587\u7ae0\u901a\u8fc7\u56de\u987e\u5f53\u524d\u7f51\u7edc\u74e6\u89e3<\/span>\uff08network dismantling\uff09<\/span>\u7684\u65b9\u6cd5\uff0c\u5c06\u73b0\u6709\u7684\u5b9e\u8bc1\u6848\u4f8b\u7814\u7a76\u5206\u4e3a\u4e09\u4e2a\u90e8\u5206\uff1a\u8bbe\u8ba1\u9c81\u68d2\u6027\u3001\u9884\u8b66\u4fe1\u53f7\u548c\u9002\u5e94\u6027\u54cd\u5e94\uff0c\u4ee5\u586b\u8865\u8fd9\u4e00\u7a7a\u767d\u3002\u5177\u4f53\u800c\u8a00\uff0c\u6211\u4eec\u9996\u5148\u4ecb\u7ecd\u5177\u6709\u64cd\u4f5c\u6027\u7684\u7f51\u7edc\u9c81\u68d2\u6027\u548c\u97e7\u6027\u7684\u7406\u8bba\u6846\u67b6\u3002\u968f\u540e\uff0c\u6211\u4eec\u63a2\u8ba8\u4e86\u590d\u6742\u7f51\u7edc\u4e0e\u6e17\u6d41\u7406\u8bba\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u5e76\u4ecb\u7ecd\u4e86\u5728\u6700\u4f18\u6e17\u6d41\u548c\u7f51\u7edc\u74e6\u89e3\u9886\u57df\u4e2d\u4f7f\u7528\u7684\u7406\u8bba\u548c\u8ba1\u7b97\u65b9\u6cd5\u3002\u6211\u4eec\u8fdb\u4e00\u6b65\u8ba8\u8bba\u4e86\u7ea7\u8054\u5931\u6548\uff0c\u4ee5\u53ca\u5bfc\u81f4\u523b\u753b\u7f51\u7edc\u7cfb\u7edf\u6027\u98ce\u9669\u4f20\u64ad\u7684\u76f8\u53d8\u53d1\u751f\u7684\u673a\u7406\u3002\u6211\u4eec\u8fd8\u8ba8\u8bba\u4e86\u9632\u6b62\u548c\u5e94\u5bf9\u7f51\u7edc\u7cfb\u7edf\u5d29\u6e83\u7684\u7b56\u7565\uff0c\u5e76\u6307\u51fa\u4e86\u672a\u6765\u53ef\u80fd\u7684\u7814\u7a76\u8d8b\u52bf\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5c3d\u7ba1\u672c\u7efc\u8ff0\u4e3b\u8981\u805a\u7126\u4e8e\u7f51\u7edc\u8282\u70b9\u7684\u79fb\u9664\uff0c\u4f46\u6240\u8ba8\u8bba\u7684\u5927\u591a\u6570\u6982\u5ff5\u3001\u5ea6\u91cf\u548c\u6280\u672f\u540c\u6837\u9002\u7528\u4e8e\u7f51\u7edc\u8fde\u8fb9\u7684\u79fb\u9664\u3002<\/span><\/section>\n

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    <\/span><\/section>\n

    \n
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    <\/svg><\/section>\n<\/section>\n<\/section>\n
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    \u4e8c\u3001\u80cc\u666f\u4fe1\u606f<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

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    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


    <\/p>\n

    \u5728\u8fd9\u7bc7\u7efc\u8ff0\u4e2d\uff0c\u6211\u4eec\u7814\u7a76\u7684\u7cfb\u7edf\u90fd\u5177\u6709\u7f51\u7edc\u7ed3\u6784\u7279\u70b9\u3002\u7f51\u7edc\u662f\u7531\u5355\u5143<\/span>\uff08\u8282\u70b9\uff09<\/span>\u901a\u8fc7\u8fb9\u6216\u5176\u4ed6\u94fe\u63a5\u65b9\u5f0f\u975e\u5e73\u51e1\u5730\u76f8\u4e92\u8fde\u63a5\u800c\u6210\u7684\u96c6\u5408\u3002\u5728\u7269\u7406\u5b66\u6587\u732e\u4e2d\uff0c\u7f51\u7edc\u4e5f\u5e38\u88ab\u63cf\u8ff0\u4e3a\u7531\u5ea7<\/span>\uff08sites\uff09<\/span>\u548c\u952e<\/span>\uff08bonds\uff09<\/span>\u7ec4\u6210\u3002\u7f51\u7edc\u53ef\u4ee5\u901a\u8fc7\u90bb\u63a5\u77e9\u9635A\u5728\u6570\u5b66\u4e0a\u8868\u793a\uff0c\u5176\u4e2d\u4efb\u610f\u5143\u7d20Aij<\/sub>\u5728\u8282\u70b9i<\/em>\u548cj<\/em>\u4e4b\u95f4\u5b58\u5728\u4ea4\u4e92\u6216\u5173\u7cfb\u65f6\u4e3a\u6b63\u503c\uff0c\u5426\u5219\u4e3a\u96f6\u3002\u5728\u5fae\u89c2\u5c42\u9762\uff0c\u4e00\u4e2a\u5e38\u7528\u7684\u8fde\u63a5\u5ea6\u91cf\u662f\u8282\u70b9\u7684\u5ea6\u6570ki<\/sub>\uff0c\u7528\u4e8e\u91cf\u5316\u4e0e\u8282\u70b9i<\/em>\u76f8\u5173\u8054\u7684\u8fde\u8fb9\u6570\u76ee\uff0c\u800c\u66f4\u590d\u6742\u7684\u63cf\u8ff0\u7b26\u5219\u88ab\u7528\u6765\u6355\u6349\u5404\u79cd\u7f51\u7edc\u7279\u5f81\uff0c\u4ece\u4e09\u89d2\u5f62\u805a\u96c6\u503e\u5411\u5230\u5355\u5143\u95f4\u4fe1\u606f\u4ea4\u6362\u7684\u4e2d\u5fc3\u6027\u7b49[3]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7406\u89e3\u7f51\u7edc\u7684\u7ed3\u6784\u548c\u529f\u80fd\u5982\u4f55\u53d7\u5230\u5355\u4e2a\u5143\u7d20<\/span>\uff08\u8282\u70b9\u548c\/\u6216\u8fb9\uff09<\/span>\u5931\u6548\u7684\u5f71\u54cd\uff0c\u662f\u4e00\u9879\u5bcc\u6709\u6311\u6218\u6027\u7684\u4efb\u52a1\u3002\u5b9e\u9645\u4e0a\uff0c\u5fae\u89c2\u5c42\u9762\u7684\u6545\u969c\u5e76\u975e\u7ebf\u6027\u7d2f\u79ef\uff0c\u867d\u7136\u5927\u90e8\u5206\u6545\u969c\u53ef\u80fd\u4e0d\u4f1a\u4e25\u91cd\u5f71\u54cd\u5e95\u5c42\u7cfb\u7edf\u7684\u529f\u80fd\uff0c\u4f46\u53bb\u9664\u7279\u5b9a\u5143\u7d20\u53ef\u80fd\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u7684\u5d29\u6e83\u3002\u7cfb\u7edf\u8f6c\u5411\u5d29\u6e83\u7684\u8fc7\u7a0b\u8d8a\u7a81\u7136\uff0c\u5c31\u8d8a\u96be\u4ee5\u6355\u6349\u9884\u8b66\u4fe1\u53f7\u6765\u9632\u6b62\u5b83\uff0c\u6216\u8bbe\u8ba1\u6709\u6548\u5e94\u5bf9\u63aa\u65bd\u6765\u51cf\u8f7b\u5176\u5f71\u54cd\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6211\u4eec\u9700\u8981\u8003\u8651\u4e00\u7cfb\u5217\u4e0d\u540c\u7684\u60c5\u666f\uff0c\u6bcf\u4e2a\u60c5\u666f\u90fd\u6709\u4e0d\u540c\u7684\u542b\u4e49\u3002\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u53ef\u4ee5\u5047\u8bbe\u5185\u90e8\u6545\u969c\u662f\u968f\u673a\u5206\u5e03\u7684\uff0c\u6bd4\u5982\u7531\u4e00\u4e2a\u8282\u70b9<\/span>\uff08\u4f8b\u5982\u8def\u7531\u5668\uff09<\/span>\u6216\u4e00\u6761\u8fb9<\/span>\uff08\u6bd4\u5982\u901a\u4fe1\u901a\u9053\uff09<\/span>\u6545\u969c\u5f15\u8d77[29]\u3002\u4f46\u7531\u4e8e\u5927\u591a\u6570\u771f\u5b9e\u4e16\u754c\u7f51\u7edc\u5177\u6709\u9ad8\u5ea6\u5f02\u8d28\u7684\u8fde\u901a\u6027[4]\uff0c\u5b83\u4eec\u901a\u5e38\u80fd\u591f\u62b5\u6297\u6b64\u7c7b\u968f\u673a\u6545\u969c\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u7f51\u7edc\u7ed3\u6784\u53ef\u80fd\u88ab\u4ee3\u7406\u5229\u7528\uff0c\u4ee5\u901a\u8fc7\u6709\u9488\u5bf9\u6027\u7684\u653b\u51fb\u6765\u84c4\u610f\u7834\u574f\u7cfb\u7edf\uff0c\u5982\u5b9e\u65bd\u514d\u75ab\u7b56\u7565[64]\u3001\u6253\u51fb\u72af\u7f6a\u7f51\u7edc\u3001\u865a\u5047\u4fe1\u606f\u6216\u6076\u610f\u8f6f\u4ef6\u7f51\u7edc[65,66]\uff0c\u4ee5\u53ca\u5bf9\u7535\u529b\u548c\u5929\u7136\u6c14\u5206\u914d\u7cfb\u7edf\u7684\u6076\u610f\u653b\u51fb\u7b49[67,68]\u3002\u4f46\u662f\uff0c\u6bcf\u6b21\u653b\u51fb\u90fd\u6709\u5176\u56fa\u6709\u6210\u672c\uff0c\u8fd9\u53d6\u51b3\u4e8e\u7279\u5b9a\u7cfb\u7edf\uff0c\u56e0\u4e3a\u79fb\u9664\u4e00\u4e2a\u8282\u70b9\u6216\u8fb9\u5bf9\u5e94\u4e8e\u4e00\u4e2a\u884c\u52a8\uff0c\u6bd4\u5982\u63a5\u79cd\u75ab\u82d7\u3001\u902e\u6355\u6216\u5173\u95ed\u670d\u52a1\u5668\u3002\u56e0\u6b64\uff0c\u7f51\u7edc\u74e6\u89e3\u7684\u76ee\u6807\u662f\u901a\u8fc7\u79fb\u9664\u5c3d\u53ef\u80fd\u5c11\u7684\u8282\u70b9\u548c\/\u6216\u8fb9\u6765\u8fbe\u5230\u65e2\u5b9a\u76ee\u6807\uff0c\u4ece\u800c\u6700\u5c0f\u5316\u6210\u672c\u3002\u5728\u6570\u5b66\u4e0a\uff0c\u8fd9\u4e00\u8fc7\u7a0b\u8f6c\u5316\u4e3a\u8bbe\u8ba1\u4e00\u4e2a\u79fb\u9664\u7b97\u6cd5\u548c\u4e00\u4e2a\u9700\u8981\u76f8\u5e94\u4f18\u5316\u7684\u6210\u672c\u51fd\u6570\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u9057\u61be\u7684\u662f\uff0c\u5373\u4f7f\u5728\u5c0f\u578b\u7f51\u7edc\u4e0a\uff0c\u627e\u51fa\u6700\u4f18\u7684\u76ee\u6807\u8282\u70b9\u6216\u8fde\u8fb9\u4e5f\u662f\u4e00\u9879\u6311\u6218\u6027\u7684\u4efb\u52a1\u3002\u4e00\u6b21\u5168\u9762\u7684\u641c\u7d22\u9700\u8981\u63a2\u7d22\u6240\u6709\u53ef\u80fd\u79fb\u9664\u7684\u8282\u70b9\u548c\/\u6216\u8fb9\u7684\u7ec4\u5408\u3002\u8fd9\u4e2a\u64cd\u4f5c\u968f\u7740\u7cfb\u7edf\u89c4\u6a21\u5448\u6307\u6570\u7ea7\u589e\u957f\uff0c\u56e0\u4e3a\u7834\u574f\u7cfb\u7edf\u6240\u9700\u79fb\u9664\u7684\u5355\u5143\u6570\u91cf\u5e76\u975e\u4e8b\u5148\u5c31\u80fd\u77e5\u9053[69]\u3002\u6bd4\u5982\uff0c\u5728\u4e00\u4e2a\u53ea\u670950\u4e2a\u8282\u70b9\u7684\u5c0f\u578b\u7f51\u7edc\u4e2d\uff0c\u8981\u627e\u5230\u6700\u4f18\u7684\u8282\u70b9\u96c6\u5408\u53ef\u80fd\u9700\u8981\u6d4b\u8bd5\u5927\u7ea6250<\/sup> \u2248 1015<\/sup>\u79cd\u7ec4\u5408\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u56e0\u6b64\uff0c\u8fd9\u4e00\u76f8\u5e94\u7684\u7ec4\u5408\u4f18\u5316\u95ee\u9898\uff0c\u5373\u7f51\u7edc\u74e6\u89e3\uff0c\u88ab\u5f52\u7c7b\u4e3aNP-\u96be\u95ee\u9898<\/span>\uff08\u5373\u65e0\u6cd5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u6c42\u5f97\u6700\u4f18\u89e3\uff09<\/span>\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\uff0c\u901a\u5e38\u91c7\u7528\u591a\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\uff0c\u5305\u62ec\u5e94\u7528\u8fd1\u4f3c\u7406\u8bba\u6a21\u578b\u548c\u8ba1\u7b97\u542f\u53d1\u5f0f\u7b97\u6cd5\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6b64\u5916\uff0c\u5728\u6587\u732e\u4e2d\u5bf9\u4e8e\u5982\u4f55\u8861\u91cf\u7cfb\u7edf\u5065\u5eb7\u72b6\u51b5\u6216\u786e\u5b9a\u7f51\u7edc\u74e6\u89e3\u7684\u76ee\u6807\uff0c\u5373\u653b\u51fb\u7684\u5177\u4f53\u76ee\u7684\uff0c\u5c1a\u65e0\u666e\u904d\u5171\u8bc6\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u5e94\u8be5\u5982\u4f55\u91cf\u5316\u8fc4\u4eca\u4e3a\u6b62\u5bf9\u7cfb\u7edf\u9020\u6210\u7684\u635f\u5bb3\uff0c\u4ee5\u4fbf\u505c\u6b62\u653b\u51fb\uff1f\u5728\u7f51\u7edc\u74e6\u89e3\u8fc7\u7a0b\u4e2d\uff0c\u53c8\u5e94\u4f18\u5316\u54ea\u4e9b\u529f\u80fd\u5462\uff1f\u5728\u635f\u5bb3\u8861\u91cf\u65b9\u9762\uff0c\u6700\u5e38\u89c1\u7684\u65b9\u6cd5\u662f\u5e94\u7528\u4e0e\u6e17\u6d41\u76f8\u5173\u7684\u6307\u6807\uff0c\u5982\u76d1\u63a7\u6700\u5927\u8fde\u901a\u7247<\/span>\uff08largest connected component \uff0cLCC\uff09<\/span>\u7684\u5927\u5c0f\uff0c\u5e76\u5728\u5176\u8fbe\u5230\u9884\u5b9a\u76ee\u6807\u5927\u5c0f\u65f6\u505c\u6b62\u653b\u51fb[70]\u3002\u6b64\u5916\uff0c\u4e5f\u6709\u7814\u7a76\u5229\u7528\u5176\u4ed6\u7f51\u7edc\u6307\u6807\uff0c\u5982\u7f51\u7edc\u6548\u7387[59,71]\u6216\u5d4c\u5957\u6027[50,51,72]\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u7f51\u7edc\u74e6\u89e3\u8fc7\u7a0b\u540e\u8fde\u901a\u7247\u7684\u7406\u60f3\u5927\u5c0f\uff0c\u4e5f\u5e76\u65e0\u5171\u8bc6\u3002\u5b9e\u9645\u4e0a\uff0c\u8868\u5f81\u7cfb\u7edf\u5931\u6548\u7684\u5927\u5c0f<\/span>\uff08\u65e0\u8bba\u662f\u76f8\u5bf9\u8fd8\u662f\u7edd\u5bf9\u5927\u5c0f\uff09<\/span>\u5f88\u5927\u7a0b\u5ea6\u4e0a\u53d6\u51b3\u4e8e\u7cfb\u7edf\u672c\u8eab\u53ca\u5176\u5e94\u7528\u573a\u666f[4,66,68,69,73]\u3002\u5728\u4f18\u5316\u76ee\u6807\u65b9\u9762\uff0c\u4e0d\u540c\u7684\u7814\u7a76\u6709\u4e0d\u540c\u7684\u7126\u70b9\uff0c\u6709\u4e9b\u65e8\u5728\u5bfb\u627e\u53ef\u80fd\u7684\u6700\u5c0f\u8282\u70b9\u96c6\u5408[29,69]\uff0c\u6709\u4e9b\u5219\u81f4\u529b\u4e8e\u5728\u653b\u51fb\u5f00\u59cb\u540e\u5c3d\u53ef\u80fd\u51cf\u5c0fLCC\u7684\u5927\u5c0f[68]\uff0c\u8fd8\u6709\u4e9b\u5219\u5173\u6ce8\u4e8e\u964d\u4f4e\u7f51\u7edc\u74e6\u89e3\u7684\u6210\u672c[66]\uff0c\u56e0\u4e3a\u67d0\u4e9b\u8282\u70b9\u7684\u79fb\u9664\u53ef\u80fd\u6bd4\u5176\u4ed6\u8282\u70b9\u66f4\u5177\u6210\u672c\u3002\u8fd9\u4e9b\u76ee\u6807\u5e76\u4e0d\u603b\u662f\u76f8\u5bb9\u7684\uff0c\u4e14\u76ee\u6807\u7684\u9009\u62e9\u8fd8\u53d6\u51b3\u4e8e\u7279\u5b9a\u5e94\u7528\u548c\u653b\u51fb\u671f\u95f4\u53ef\u7528\u7684\u8d44\u6e90\uff0c\u5982\u65f6\u95f4\u6216\u8d44\u91d1\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u53e6\u4e00\u4e2a\u9700\u8981\u8003\u8651\u7684\u95ee\u9898\u662f\u653b\u51fb\u7b97\u6cd5\u672c\u8eab\u7684\u8ba1\u7b97\u6210\u672c\uff0c\u8fd9\u53ef\u4ee5\u901a\u8fc7\u7b97\u6cd5\u7684\u8fd0\u884c\u65f6\u95f4\u548c\u5185\u5b58\u4f7f\u7528\u91cf\u6765\u8861\u91cf\u3002\u8ba1\u7b97\u590d\u6742\u5ea6<\/span>\uff08\u6216\u65f6\u95f4\u590d\u6742\u5ea6\uff09<\/span>[74]\u63d0\u4f9b\u4e86\u4e00\u79cd\u8861\u91cf\u7b97\u6cd5\u89e3\u51b3\u95ee\u9898\u6240\u9700\u65f6\u95f4\u7684\u65b9\u6cd5\uff0c\u56e0\u6b64\u53ef\u4ee5\u7528\u6765\u4e25\u683c\u6bd4\u8f83\u4e0d\u540c\u7b97\u6cd5\u7684\u6548\u7387\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u4e3b\u8981\u5047\u8bbe\u662f\u7b97\u6cd5\u7684\u8fd0\u884c\u65f6\u95f4\u4e0e\u5176\u6267\u884c\u7684\u57fa\u672c\u64cd\u4f5c\u6570\u91cf\u6210\u6b63\u6bd4\uff0c\u8fd9\u4e9b\u64cd\u4f5c\u6570\u91cf\u4ee5\u8f93\u5165\u5927\u5c0f\u7684\u51fd\u6570\u5f62\u5f0f\u8868\u8fbe\uff0c\u5e76\u4e14\u5047\u8bbe\u6240\u6709\u7c7b\u578b\u7684\u64cd\u4f5c\u6240\u9700\u65f6\u95f4\u76f8\u540c\u3002\u5c3d\u7ba1\u8fd9\u4e2a\u5047\u8bbe\u5e76\u975e\u5b8c\u5168\u51c6\u786e\uff0c\u4f46\u5b83\u662f\u8861\u91cf\u968f\u7740\u8f93\u5165\u5927\u5c0f\u589e\u52a0\u6240\u9700\u65f6\u95f4\u5982\u4f55\u53d8\u5316\u7684\u826f\u597d\u8fd1\u4f3c\uff0c\u5e76\u4e14\u4e0d\u53d7\u786c\u4ef6\u3001\u8f6f\u4ef6\u6216\u7f16\u7a0b\u8bed\u8a00\u914d\u7f6e\u7684\u5177\u4f53\u5f71\u54cd\u2014\u2014\u7406\u8bba\u4e0a\uff0c\u6bcf\u4e2a\u7b97\u6cd5\u81f3\u5c11\u53ef\u4ee5\u6784\u5efa\u4e00\u4e2a\u4f18\u5316\u914d\u7f6e\u3002\u7279\u522b\u662f\uff0c\u5e38\u7528\u4e8e\u6bd4\u8f83\u7684\u5927O\u7b26\u53f7[74]\uff0c\u8868\u793a\u4f5c\u4e3a\u8f93\u5165\u5927\u5c0f\u7684\u51fd\u6570\u65f6\u6267\u884c\u7684\u64cd\u4f5c\u6570\u91cf\u7684\u6e10\u8fd1\u503c\uff0c\u5e76\u9664\u975e\u53e6\u6709\u660e\u786e\u8bf4\u660e\uff0c\u901a\u5e38\u6307\u7684\u662f\u6700\u574f\u60c5\u51b5\u3002\u5b9e\u9645\u4e0a\uff0c\u6700\u4f18\u60c5\u51b5\u901a\u5e38\u4e0e\u7b80\u5355\u7684\u5b9e\u4f8b\u76f8\u5173\uff0c\u56e0\u6b64\u5e76\u4e0d\u91cd\u8981\uff0c\u800c\u5e73\u5747\u60c5\u51b5\u5219\u901a\u5e38\u96be\u4ee5\u8ba1\u7b97\uff0c\u56e0\u4e3a\u5b83\u53d6\u51b3\u4e8e\u7279\u5b9a\u7684\u8f93\u5165\u548c\u7b97\u6cd5\u8def\u5f84\u3002\u4f8b\u5982\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(N)\u8868\u793a\u7ed9\u5b9a\u8f93\u5165\u5927\u5c0fN\u65f6\uff0c\u7b97\u6cd5\u6267\u884cN\u6b21\u64cd\u4f5c\uff0c\u800cO(N2<\/sup>)\u8868\u793a\u6267\u884cN<\/span>2<\/sup>\u6b21\u64cd\u4f5c\u3002\u5bf9\u7a7a\u95f4\u590d\u6742\u5ea6\u7684\u8003\u91cf\u4e5f\u7c7b\u4f3c\uff0c\u5b83\u8861\u91cf\u5185\u5b58\u4f7f\u7528\u91cf\u5982\u4f55\u968f\u8f93\u5165\u5927\u5c0f\u53d8\u5316\u3002\u7136\u800c\uff0c\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u7531\u4e8e\u7a7a\u95f4\u590d\u6742\u5ea6\u901a\u5e38\u4e0d\u662f\u7b97\u6cd5\u7684\u9650\u5236\u56e0\u7d20\uff0c\u6240\u4ee5\u6587\u732e\u4e2d\u901a\u5e38\u4e0d\u8003\u8651\u7a7a\u95f4\u590d\u6742\u5ea6\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u63a5\u4e0b\u6765\u7684\u90e8\u5206\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8\u524d\u8ff0\u7406\u8bba\u95ee\u9898\u4e0e\u6e17\u6d41\u7406\u8bba\u4e4b\u95f4\u7684\u76f4\u63a5\u8054\u7cfb\u3002\u6e17\u6d41\u7406\u8bba\u662f\u7edf\u8ba1\u7269\u7406\u4e2d\u5e7f\u6cdb\u5e94\u7528\u7684\u6846\u67b6\uff0c\u7528\u4e8e\u7814\u7a76\u7cfb\u7edf\u7684\u884c\u4e3a\u53ca\u5176\u5bf9\u6270\u52a8\u7684\u4e34\u754c\u53cd\u5e94\u3002<\/span><\/section>\n

    <\/section>\n

    <\/section>\n

    \n
    \n
    \n
    \n
    \n

    <\/section>\n

    <\/section>\n
    \n
    <\/svg><\/section>\n<\/section>\n<\/section>\n
    \n

    \u4e09\u3001\u4e0e\u6e17\u6d41\u7406\u8bba\u7684\u8054\u7cfb<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


    <\/p>\n

    \u6e17\u6d41\u7406\u8bba\u65e0\u7591\u662f\u5904\u7406\u7f51\u7edc\u74e6\u89e3\u95ee\u9898\u6700\u76f4\u63a5\u548c\u6700\u76f4\u89c2\u7684\u6846\u67b6\uff0c\u56e0\u6b64\u4e5f\u662f\u88ab\u7814\u7a76\u5f97\u6700\u591a\u7684\u3002\u8fd9\u4e2a\u8457\u540d\u6a21\u578b\u6700\u521d\u5728\u51dd\u80f6\u7814\u7a76\u4e2d\u7406\u8bba\u4e0a\u88ab\u63d0\u51fa[75]\uff0c\u540e\u6765\u5728\u7edf\u8ba1\u7269\u7406[32,76]\u548c\u6982\u7387\u8bba[77]\u9886\u57df\u8fdb\u4e00\u6b65\u53d1\u5c55\uff0c\u5e76\u5728\u79d1\u5b66\u548c\u5de5\u7a0b\u7684\u5404\u4e2a\u9886\u57df\u5f97\u5230\u5e7f\u6cdb\u5e94\u7528[78-80]\u3002\u6e17\u6d41\u53ef\u4ee5\u89c6\u4e3a\u4e00\u79cd\u5b9e\u9a8c\uff0c\u5728\u6b64\u5b9e\u9a8c\u4e2d\uff0c\u6839\u636e\u4e00\u4e9b\u9884\u5b9a\u4e49\u7684\u89c4\u5219<\/span>\uff08\u4e5f\u79f0\u4e3a\u653b\u51fb\u7b56\u7565\uff0cattacking protocols\uff09<\/span>\u79fb\u9664\u8282\u70b9\u548c\/\u6216\u8fde\u8fb9\uff0c\u7136\u540e\u8ba1\u7b97\u5269\u4f59\u7f51\u7edc\u7684\u4e0d\u540c\u7edf\u8ba1\u548c\u51e0\u4f55\u5c5e\u6027<\/span>\uff08\u89c1\u56fe1a\uff09<\/span>\u3002\u8fd9\u79cd\u65b9\u6cd5\u5141\u8bb8\u6211\u4eec\u5728\u7cfb\u7edf\u7ec4\u5206\u56e0\u67d0\u79cd\u539f\u56e0<\/span>\uff08\u5982\u6545\u969c\u3001\u7ef4\u6301\u3001\u653b\u51fb\u7b49\uff09<\/span>\u5931\u6548\u65f6\uff0c\u8ffd\u8e2a\u7cfb\u7edf\u7684\u7ed3\u6784\u54cd\u5e94\u3002\u8fd9\u4e9b\u7ec4\u4ef6\u7684\u72b6\u6001\u88ab\u89c6\u4e3a\u4e8c\u5143\u7684\uff1a\u5b58\u5728<\/span>\uff08\u529f\u80fd\u6b63\u5e38\uff09<\/span>\u6216\u79fb\u9664<\/span>\uff08\u5df2\u5931\u6548\uff09<\/span>\uff0c\u901a\u5e38\u4f1a\u8ba1\u7b97\u7531\u529f\u80fd\u6b63\u5e38\u8282\u70b9\u5f62\u6210\u7684\u5269\u4f59\u8fde\u901a\u7247\u7684\u5927\u5c0f\u3002\u6e17\u6d41\u7406\u8bba\u4e0e\u7f51\u7edc\u74e6\u89e3\u4e4b\u95f4\u7684\u5bcc\u6709\u6210\u6548\u7684\u8054\u7cfb\u6e90\u81ea\u4e8e\u8fd9\u6837\u4e00\u4e2a\u5047\u8bbe\uff1a\u4e00\u4e2a\u7cfb\u7edf\u8981\u6b63\u5e38\u8fd0\u884c\uff0c\u65e0\u8bba\u5176\u529f\u80fd\u5982\u4f55\uff0c\u5fc5\u987b\u5168\u5c40\u8fde\u901a\u3002\u56e0\u6b64\uff0c\u7f51\u7edc\u9000\u5316\u5bfc\u81f4\u7684\u529f\u80fd\u635f\u5931\u53ef\u4ee5\u6620\u5c04\u5230\u6e17\u6d41\u6a21\u578b\u7684\u76f8\u53d8\u8fc7\u7a0b\u3002\u5728\u64cd\u4f5c\u4e0a\uff0c\u8fd9\u901a\u5e38\u901a\u8fc7\u8bf8\u5982\u4e34\u754c\u70b9\u548c\u6700\u5927\u8fde\u901a\u7247<\/span>\uff08LCC\uff0c\u5728\u70ed\u529b\u5b66\u6781\u9650\u4e0b\u4e5f\u88ab\u79f0\u4e3a\u5de8\u7ec4\u5206\uff08<\/span>giant component\uff09\uff09<\/span>\u7684\u5927\u5c0f\u6765\u65b9\u4fbf\u5730\u8868\u5f81\uff0c\u4ece\u800c\u63d0\u4f9b\u5bf9\u7f51\u7edc\u74e6\u89e3\u8fc7\u7a0b\u7684\u5b9a\u91cf\u548c\u5b9a\u6027\u6d1e\u5bdf<\/span>\uff08\u89c1\u56fe1b-d\uff09<\/span>\u3002<\/span><\/section>\n

    <\/section>\n
    <\/section>\n

    \u56fe1 \u6e17\u6d41\u4f5c\u4e3a\u7f51\u7edc\u9c81\u68d2\u6027\u7684\u9759\u6001\u65b9\u6cd5\u3002a\u3001\u7531\u4e8e\u6839\u636e\u9884\u5b9a\u4e49\u7684\u79fb\u9664\u534f\u8bae\u03a6<\/span>\u9009\u62e9\u4e86\u4e00\u4e9b\u8282\u70b9\uff08\u7070\u8272\u8282\u70b9\uff09\uff0c\u7f51\u7edc\u89e3\u4f53\u3002\u5e72\u9884\u7684\u7ed3\u679c\u662f\u7f51\u7edc\u5206\u88c2\u6210\u4e09\u4e2a\u8fde\u901a\u7247\uff0c\u5b83\u4eec\u7684\u5927\u5c0f\u5206\u522b\u4e3aS1<\/sub>\u3001S2<\/sub>\u548cS3<\/sub>\u3002\u8fd9\u4e9b\u7c07\u5927\u5c0f\u662f\u6e17\u6d41\u7814\u7a76\u4e2d\u7684\u4e00\u4e2a\u6838\u5fc3\u91cf\u3002b-d\u3001\u03a6<\/span>\u7684\u6027\u8d28\u4e0e\u63a7\u5236\u53c2\u6570\u76f8\u5173\uff0c\u4e25\u91cd\u5f71\u54cd\u7f51\u7edc\u7684\u54cd\u5e94\uff0c\u5bfc\u81f4\u6700\u5927\u8fde\u901a\u7247\u5927\u5c0f\u7684\u4e0d\u540c\u7c7b\u578b\u7684\u76f8\u53d8\u3002e\u3001\u5177\u6709\u5747\u5300\u548c\u5f02\u8d28\u8fde\u63a5\u6a21\u5f0f\u7684\u7f51\u7edc\uff08\u7c97\u7565\u5730\u8bf4\uff0c\u5ea6\u5206\u5e03\u7684\u4e8c\u9636\u77e9\u4e0e\u5e73\u5747\u503c\u7684\u5e73\u65b9\u76f8\u5f53\u6216\u8fdc\u5927\u4e8e\u5e73\u5747\u503c\uff09\u5bf9\u6545\u969c\u548c\u6709\u9488\u5bf9\u6027\u7684\u653b\u51fb\u7684\u54cd\u5e94\u65b9\u5f0f\u3002\u5706\u5708\u4ee3\u8868\u8fde\u901a\u5206\u91cf\uff0c\u5176\u534a\u5f84\u53d6\u51b3\u4e8e\u5176\u8282\u70b9\u6570\u91cf\u3002\u6bcf\u4e2a\u5782\u76f4\u5217\u5047\u8bbe\u5220\u9664\u76f8\u540c\u6570\u91cf\u7684\u8282\u70b9\u6216\u94fe\u63a5\u3002e\u90e8\u5206\u6539\u7f16\u81ea\u53c2\u8003\u6587\u732e[225]\u3002<\/span><\/p>\n


    <\/span><\/section>\n
    \u5728\u590d\u6742\u7f51\u7edc\u4e2d\uff0c\u8282\u70b9\u5728\u7ed3\u6784\u6216\u529f\u80fd\u4e0a\u5e76\u4e0d\u5982\u89c4\u5219\u6676\u683c<\/span>\uff08Regular Lattices\uff09<\/span>\u4e2d\u7684\u8282\u70b9\u90a3\u6837\u540c\u8d28\u3002\u5b58\u5728\u5927\u91cf\u7684\u65b9\u6cd5\u548c\u5ea6\u91cf\u6807\u51c6\uff0c\u53ef\u4ee5\u6839\u636e\u4e0d\u540c\u7684\u6807\u51c6\u5bf9\u8282\u70b9\u8fdb\u884c\u6392\u5e8f\uff0c\u8fd9\u4e9b\u901a\u5e38\u662f\u7531\u5177\u4f53\u5e94\u7528\u9a71\u52a8\u7684\u3002\u8fd9\u79cd\u5185\u5728\u7684\u5f02\u8d28\u6027\u63d0\u4f9b\u4e86\u591a\u79cd\u653b\u51fb\u7b56\u7565\u7684\u9009\u62e9\uff0c\u4ece\u800c\u4f7f\u6211\u4eec\u80fd\u591f\u5728\u8bb8\u591a\u4e0e\u7269\u7406\u5b66\u76f8\u5173\u7684\u573a\u666f\u4e0b\u8bc4\u4f30\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u3002\u4f8b\u5982\uff0c\u968f\u673a\u9009\u62e9\u8282\u70b9\u7684\u65b9\u6cd5\u88ab\u7528\u6765\u6a21\u62df\u7cfb\u7edf\u4e2d\u53d1\u751f\u7684\u6545\u969c\u548c\u9519\u8bef\uff0c\u800c\u66f4\u7cbe\u7ec6\u5316\u7684\u9488\u5bf9\u6027\u653b\u51fb\u5219\u53ef\u4ee5\u4f5c\u4e3a\u6709\u4fe1\u606f\u7684\u5e72\u9884\u63aa\u65bd\u6765\u6267\u884c\u3002\u8fd9\u79cd\u5e72\u9884\u53ef\u80fd\u57fa\u4e8e\u62d3\u6251\u4fe1\u606f\uff0c\u4f8b\u5982\u79fb\u9664\u5177\u6709\u6700\u591a\u8fde\u8fb9\u6216\u6700\u5927\u4e2d\u5fc3\u6027\u7684\u8282\u70b9[81,82]\uff0c\u6216\u8005\u57fa\u4e8e\u975e\u62d3\u6251\u4fe1\u606f\uff0c\u4f8b\u5982\u6839\u636e\u8282\u70b9\u6216\u8fde\u8fb9\u7684\u5143\u6570\u636e\u6765\u8fdb\u884c\u5e72\u9884[83]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7f51\u7edc\u74e6\u89e3\u7b56\u7565\u4e0e\u7f51\u7edc\u62d3\u6251\u4e4b\u95f4\u7684\u4ea4\u4e92\u662f\u975e\u5e73\u51e1\u7684\u3002\u65e0\u8bba\u662f\u5728\u4eba\u5de5\u7f51\u7edc\u8fd8\u662f\u5728\u5b9e\u8bc1\u7f51\u7edc\u4e2d\uff0c\u540c\u8d28\u6216\u5f02\u8d28\u7684\u8fde\u63a5\u6a21\u5f0f\u90fd\u53ef\u80fd\u5f15\u53d1\u622a\u7136\u4e0d\u540c\u7684\u53cd\u5e94[29]<\/span>\uff08\u89c1\u56fe1e\uff09<\/span>\u3002\u7531\u4e8e\u540c\u8d28\u7f51\u7edc\u4e2d\u6700\u5927\u53ef\u80fd\u7684\u8282\u70b9\u5ea6\u6570\u4e0e\u5e73\u5747\u503c\u76f8\u8fd1\uff0c\u5b83\u4eec\u5bf9\u6545\u969c\u548c\u653b\u51fb\u7684\u53cd\u5e94\u76f8\u4f3c\uff0c\u603b\u80fd\u627e\u5230\u4e00\u4e2a\u6709\u9650\u74e6\u89e3\u70b9<\/span>\uff08\u89c1\u56fe1e\uff09<\/span>\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u5f02\u8d28\u7f51\u7edc\uff0c\u5982\u65e0\u6807\u5ea6\u7f51\u7edc\uff0c\u7531\u4e8e\u67a2\u7ebd\u8282\u70b9\u7684\u4f5c\u7528\uff0c\u6545\u969c\u548c\u653b\u51fb\u4f1a\u5bfc\u81f4\u4e0d\u540c\u7684\u54cd\u5e94\u3002\u5f53\u6545\u969c\u968f\u673a\u53d1\u751f\u65f6\uff0c\u67a2\u7ebd\u8282\u70b9\u975e\u5e38\u6709\u6548\u5730\u7ef4\u6301\u7740\u7f51\u7edc\u7684\u8fde\u901a\u6027\uff0c\u4f46\u5982\u679c\u8282\u70b9\u4f5c\u4e3a\u76ee\u6807\u88ab\u76f4\u63a5\u653b\u51fb\uff0c\u5219\u7f51\u7edc\u4f1a\u8fc5\u901f\u5206\u88c2\u2014\u2014\u8fd9\u5c31\u662f\u5f02\u8d28\u7f51\u7edc\u6240\u7279\u6709\u7684\u201c\u9c81\u68d2\u800c\u8106\u5f31\u201d <\/span>\uff08robust-yet-fragile\uff09<\/span>\u7684\u7279\u6027<\/span>\uff08\u89c1\u56fe1e\uff09<\/span>\u3002\u540c\u8d28\u7f51\u7edc\u548c\u5f02\u8d28\u7f51\u7edc\u4e4b\u95f4\u7684\u8fd9\u79cd\u5dee\u5f02\u4e0e\u975e\u76f8\u5173\u7f51\u7edc\u4e2d\u74e6\u89e3\u70b9\u7684\u9884\u6d4b\u4e00\u81f4[84,85]\uff1b\u5e76\u4e14\u5df2\u7ecf\u901a\u8fc7\u57fa\u4e8e\u751f\u6210\u51fd\u6570<\/span>\uff08generating functions\uff09<\/span>\u7684\u7406\u8bba\u65b9\u6cd5\u5f97\u5230\u4e86\u66f4\u7cfb\u7edf\u548c\u5b9a\u91cf\u7684\u63cf\u8ff0\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4f9d\u8d56\u751f\u6210\u51fd\u6570\u7684\u65b9\u6cd5\u4f18\u52bf\u5728\u4e8e\u5176\u6570\u5b66\u4e0a\u7684\u7075\u6d3b\u6027\uff0c\u80fd\u591f\u5305\u542b\u66f4\u5e7f\u6cdb\u7684\u60c5\u51b5\uff0c\u540c\u65f6\u5bf9\u4e34\u754c\u6307\u6570\u63d0\u4f9b\u4e00\u5b9a\u7684\u9884\u6d4b\u529b[85,90,91]\uff0c\u6216\u8005\u5bf9\u4e34\u754c\u70b9\u548c\u6700\u5927\u8fde\u901a\u7247\u5927\u5c0f\u63d0\u4f9b\u5c01\u95ed\u5f62\u5f0f\u7684\u516c\u5f0f<\/span>\uff08Closed-form equations\uff09<\/span>[92]\u3002\u8fd9\u4e9b\u65b9\u6cd5\u5047\u8bbe\u5e95\u5c42\u7f51\u7edc\u662f\u914d\u7f6e\u6a21\u578b<\/span>\uff08configurational model\uff09<\/span>\u7684\u9000\u706b\u7248\u672c\uff0c\u56e0\u6b64\u5728\u7cfb\u7efc\u7ea7\u522b\u5904\u7406\u7f51\u7edc\u9c81\u68d2\u6027\uff0c\u5e76\u6709\u52a9\u4e8e\u63ed\u793a\u5ea6\u5206\u5e03pk<\/sub>\u6216\u5176\u53c2\u6570\u6240\u8d77\u7684\u4f5c\u7528\u3002\u4f8b\u5982\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u8282\u70b9\u79fb\u9664\u534f\u8bae<\/span>\u03a6<\/span>k<\/sub>\u4e0e\u5ea6\u6570\u76f8\u5173\uff0c\u90a3\u4e48\u6700\u5927\u8fde\u901a\u7247\u7684\u5927\u5c0fSGF<\/sup>\u7531\u4ee5\u4e0b\u65b9\u7a0b\u6c42\u89e3\u5f97\u51fa\uff1a<\/span><\/section>\n

    <\/section>\n

    <\/p>\n


    <\/section>\n
    \u5176\u4e2d\uff0c<\/sub><\/span>\u548c<\/sub><\/span>\u662f\u5ea6\u5206\u5e03\u548c\u5269\u4f59\u5ea6\u5206\u5e03\u7684\u751f\u6210\u51fd\u6570\u3002<\/span>\uff08\u8d85\u989d\u5ea6\uff08excess degree\uff09\u662f\u4e00\u4e2a\u8282\u70b9\u968f\u673a\u9009\u62e9\u7684\u90bb\u5c45\u7684\u8fde\u63a5\u6570\u51cf\u4e00\u3002\uff09<\/span>\u3008k<\/span>\u3009\u8868<\/span>\u793a\u5e73\u5747\u5ea6\u3002\u7f51\u7edc\u74e6\u89e3\u70b9\u7531\u76f8\u5e94\u7684\u65b9\u7a0b\u7ed9\u51fa\u3002\u7c7b\u4f3c\u7684\u65b9\u7a0b\u4e5f\u53ef\u4ee5\u7528\u4e8e\u968f\u673a\u8fde\u8fb9\u6545\u969c\u7684\u60c5\u5f62[93]\u3002\u901a\u8fc7\u8fd9\u4e9b\u65b9\u7a0b\uff0c\u6211\u4eec\u53ef\u4ee5\u8f7b\u6613\u9a8c\u8bc1\u5728\u5ea7\u6e17\u6d41<\/span>\uff08\u79fb\u9664\u8282\u70b9\uff09<\/span>\u548c\u952e\u6e17\u6d41<\/span>\uff08\u79fb\u9664\u94fe\u63a5\uff09<\/span>\u4e2d\uff0c\u74e6\u89e3\u70b9\u7684\u4f4d\u7f6e\u662f\u4e00\u81f4\u7684\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u53ea\u8981\u7f51\u7edc\u4e2d\u7684\u8fde\u63a5\u6a21\u5f0f\u4e0d\u662f\u7279\u522b\u5f02\u8d28\uff0c\u523b\u753b\u76f8\u53d8\u7684\u4e34\u754c\u6307\u6570\u4e5f\u662f\u4e00\u81f4\u7684\uff0c\u5e76\u4e14\u5b83\u4eec\u4e0e\u7f51\u7edc\u65e0\u5173\uff0c\u7b49\u540c\u4e8e\u5e73\u5747\u573a\u9884\u6d4b[76]\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u7ed3\u679c\u4e0d\u9002\u7528\u4e8e\u66f4\u5f02\u8d28\u7684\u7f51\u7edc\uff1a\u4f8b\u5982\uff0c\u5728\u65e0\u6807\u5ea6\u7f51\u7edc\u4e2d\uff0c\u666e\u9002\u6027\u7b49\u4ef7\u6027\u88ab\u6253\u7834[94]\uff0c\u4e14\u4e34\u754c\u6307\u6570\u53ef\u80fd\u4f9d\u8d56\u4e8e\u5ea6\u5206\u5e03\u7684\u6307\u6570[85]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u9488\u5bf9\u8fde\u8fb9\u7684\u5b9a\u5411\u653b\u51fb\u5728\u6587\u732e\u4e2d\u7684\u63a2\u8ba8\u76f8\u5bf9\u8f83\u5c11\u3002\u4e3a\u4e86\u5728\u74e6\u89e3\u8fc7\u7a0b\u4e2d\u7f16\u7801\u94fe\u63a5\u4fe1\u606f\uff0c\u9700\u8981\u540c\u65f6\u8003\u8651\u94fe\u63a5\u4e24\u7aef\u8282\u70b9\u7684\u62d3\u6251\u5c5e\u6027\uff0c\u8fd9\u9700\u8981\u6bd4\u4e4b\u524d\u63d0\u5230\u7684\u65b9\u6cd5\u66f4\u590d\u6742\u7684\u6570\u5b66\u5904\u7406[95]\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u8bb8\u591a\u5b9e\u8bc1\u7f51\u7edc\u662f\u52a0\u6743\u7684\uff0c\u6216\u5728\u8fde\u8fb9\u4e0a\u5b9a\u4e49\u4e86\u7279\u5f81\u548c\/\u6216\u5143\u6570\u636e\u3002\u56e0\u6b64\uff0c\u5c06\u74e6\u89e3\u95ee\u9898\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\u516c\u5f0f\u5316\uff0c\u65e0\u7591\u5c06\u662f\u6e17\u6d41\u7406\u8bba\u672a\u6765\u5e94\u7528\u7684\u4e00\u4e2a\u5bcc\u6709\u6210\u679c\u7684\u9886\u57df\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u751f\u6210\u51fd\u6570\u7528\u4ee5\u7cbe\u786e\u9884\u6d4b\u5b9e\u8bc1\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u65b9\u6cd5\u53ef\u80fd\u5e76\u4e0d\u603b\u662f\u5b9e\u7528\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u5173\u6ce8\u7684\u662f\u7279\u5b9a\u7f51\u7edc\u62d3\u6251\u5bf9\u4e8e\u6545\u969c\u7684\u54cd\u5e94\uff0c\u800c\u975e\u5173\u6ce8\u7f51\u7edc\u7684\u6574\u4f53\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6d88\u606f\u4f20\u9012\u65b9\u6cd5<\/span>\uff08message-passing methods\uff09<\/span>\u53ef\u80fd\u66f4\u4e3a\u65b9\u4fbf\uff0c\u56e0\u4e3a\u5b83\u4f7f\u7528\u7f51\u7edc\u7684\u5b9e\u9645\u8fde\u901a\u6027\u800c\u975e\u5176\u5ea6\u5206\u5e03\u4f5c\u4e3a\u8f93\u5165\uff0c\u6765\u8ba1\u7b97\u6e17\u6d41\u91cf[97-100]\u3002\u8fd9\u79cd\u65b9\u6cd5\u5bfc\u81f4\u4e86\u66f4\u590d\u6742\u7684\u6570\u5b66\u548c\u6570\u503c\u5904\u7406\uff0c\u4f46\u901a\u5e38\u80fd\u63d0\u4f9b\u6bd4\u57fa\u4e8e\u751f\u6210\u51fd\u6570\u65b9\u6cd5\u66f4\u597d\u7684\u6700\u5927\u8fde\u901a\u7247\u548c\u4e34\u754c\u70b9\u4f30\u8ba1[101,102]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u7528\u03a6<\/span>i<\/sub><\/span>\u8868\u793a\u8282\u70b9i\u672a\u88ab\u79fb\u9664\u7684\u6982\u7387\uff0c\u7f51\u7edc\u7684\u5de8\u7ec4\u5206SMP<\/sup><\/em>\u7684\u5927\u5c0f\u7531\u5982\u4e0b\u516c\u5f0f\u7ed9\u51fa\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/p>\n


    <\/section>\n
    \u5728\u6b64\uff0cSi<\/sub>\u4ee3\u8868\u8282\u70b9i\u5c5e\u4e8e\u5de8\u7ec4\u5206\u7684\u6982\u7387\uff0c <\/sub><\/span>\u8868\u793a\u8282\u70b9\u7684\u90bb\u57df\uff0c\u8282\u70b9j\u901a\u8fc7<\/span>\uff08\u6709\u5411\uff09<\/span>\u6d88\u606f\u7684\u5f62\u5f0f\u5c06\u5c5e\u4e8e\u6700\u5927\u8fde\u901a\u7247\u7684\u6982\u7387\u4f20\u9012\u7ed9\u5468\u56f4\u8282\u70b9\uff0c<\/sub><\/span>\u4ee3\u8868\u63a5\u53d7\u5230\u8282\u70b9j\u4f20\u9012\u6d88\u606f\u7684\u8282\u70b9\u5b50\u96c6\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c<\/sub><\/span>\u662f\u4e3a\u4e86\u907f\u514d\u56de\u6eaf\u4fe1\u606f\uff0c\u5c3d\u7ba1\u8003\u8651\u77ed\u7a0b\u73af\u8def\u7684\u5176\u4ed6\u9009\u62e9\u4e5f\u662f\u53ef\u80fd\u7684[102]\u3002\u5728\u63a5\u8fd1\u74e6\u89e3\u70b9\u65f6\uff0c\u6240\u6709ti\u2192j<\/sub>\u7684\u90fd\u8d8b\u5411\u4e8e0\uff0c\u6240\u4ee5\u53ef\u4ee5\u6269\u5c55\u65b9\u7a0b\uff085\uff09\u5f97\u5230<\/sub><\/span>\uff0c\u5176\u4e2d\u2218\u662fHadamard\u79ef\uff0c<\/sub><\/span> \uff0c\u6bcf\u4e2a\u03a6<\/span>i<\/sub><\/span>\u51fa\u73b0ki<\/sub><\/span>\u6b21\u3002G\u662f\u4e00\u4e2a\u7ef4\u5ea6\u4e3a2\u2223E\u2223\u2009\u00d7\u20092\u2223E\u2223 \u7684\u903b\u8f91\u77e9\u9635\uff0c\u5176\u4e2d \u2223E\u2223 \u662f\u8fde\u8fb9\u6570\uff0c\u5e76\u4e14\u5b83\u4f9d\u8d56\u4e8e<\/sub><\/span>\u3002\u74e6\u89e3\u6761\u4ef6\u7531\u5728\u7279\u5f81\u503c\u95ee\u9898<\/sub><\/span>\u4e2d\u6d8c\u73b0\u7684\u975e\u5e73\u51e1\u89e3\u51b3\u5b9a\uff0c\u5176\u4e2d<\/sub><\/span>\u662fHadamard\u9664\u6cd5\uff0c\u03bb\u662f\u7279\u5f81\u503c\u3002Perron\u2013Frobenius\u5b9a\u7406\u8868\u660e\uff0c\u975e\u5e73\u51e1\u89e3\u4e0e\u7b97\u5b50G\u7684\u6700\u5927\u7279\u5f81\u503c\u76f8\u5173\u3002\u5bf9\u4e8e\u5e38\u6570\u5360\u7528\u6982\u7387<\/span>\u03c6i<\/sub><\/span>=\u03c6<\/span>\uff0c\u53ef\u4ee5\u5f97\u5230\u03a6<\/span>c<\/sub><\/span>=1\/\u03bbmax<\/sub><\/span>\uff0c\u5176\u4e2d\u03bb<\/span>max<\/sub>\u662fG\u7684\u6700\u5927\u7279\u5f81\u503c\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6d88\u606f\u4f20\u9012\u65b9\u6cd5\u4e5f\u53ef\u4ee5\u7528\u4e8e\u952e\u6e17\u6d41\u3002\u5982\u679c\u968f\u673a\u9009\u53d6\u7684\u4e00\u90e8\u52061-\u03c6<\/span>\u7684\u8fde\u8fb9\u4ece\u7f51\u7edc\u4e2d\u79fb\u9664\uff0c\u5219\u6700\u5927\u8fde\u901a\u5206\u91cf\u7684\u5927\u5c0f\u7531\u7ed9SMP<\/sup>\/\u03c6<\/span>\u51fa\u3002\u56e0\u6b64\uff0c\u6d88\u606f\u4f20\u9012\u5bf9\u4e8e\u5ea7\u6e17\u6d41\u548c\u952e\u6e17\u6d41\u9884\u6d4b\u4e86\u76f8\u540c\u7684\u6e17\u6d41\u9608\u503c\uff0c\u8fd9\u4e0e\u57fa\u4e8e\u751f\u6210\u51fd\u6570\u7684\u9884\u6d4b\u4e00\u81f4[94]\u3002\u57fa\u4e8e\u8fde\u8fb9\u653b\u51fb\u7684\u7f51\u7edc\u74e6\u89e3\u53ef\u4ee5\u5728\u8fd9\u4e2a\u6846\u67b6\u4e0b\u8f7b\u677e\u5b9e\u73b0\uff0c\u56e0\u4e3a\u6bcf\u4e2a\u72ec\u7acb\u8fde\u8fb9\u7684\u79fb\u9664\u6982\u7387\u53ef\u4ee5\u7f16\u7801\u5728\u4e00\u4e2a\u65b0\u7684\u5360\u7528\u6982\u7387\u5411\u91cf\u03c6’<\/span>\u4e2d\uff0c\u7136\u540e\u5c06\u5176\u5e94\u7528\u4e8e\u952e\u6e17\u6d41\u7684\u6d88\u606f\u4f20\u9012\u65b9\u7a0b\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6e17\u6d41\u7406\u8bba\u8fd8\u6709\u52a9\u4e8e\u5bf9\u5448\u73b0\u51fa\u62d3\u6251\u5173\u8054\u7684\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u8fdb\u884c\u9884\u6d4b\uff0c\u8fd9\u662f\u5927\u591a\u6570\u5b9e\u8bc1\u4e92\u8fde\u7cfb\u7edf\u7684\u4e00\u4e2a\u7279\u5f81\u3002\u5176\u4e2d\u4e00\u79cd\u5173\u8054\u88ab\u79f0\u4e3a\u540c\u914d\u6df7\u5408<\/span>\uff08assortative mixing\uff09<\/span>[103]\uff0c\u5373\u8282\u70b9\u503e\u5411\u4e8e\u4e0e\u76f8\u4f3c\u7c7b\u578b\u7684\u8282\u70b9\u76f8\u8fde\u3002\u5728\u5ea6\u6570\u4e0a\u540c\u914d\u7684\u7f51\u7edc\u6bd4\u90a3\u4e9b\u4e0d\u540c\u914d\u6a21\u5f0f\u7684\u7f51\u7edc\u66f4\u4e3a\u9c81\u68d2\uff0c\u56e0\u4e3a\u67a2\u7ebd\u8282\u70b9\u521b\u5efa\u4e86\u4e00\u4e2a\u5728\u968f\u673a\u653b\u51fb\u6216\u67a2\u7ebd\u653b\u51fb\u9762\u524d\u80fd\u591f\u7ef4\u6301\u7f51\u7edc\u8fde\u901a\u6027\u7684\u5197\u4f59\u6838\u5fc3[104]\u3002\u5c40\u90e8\u805a\u7c7b\u7684\u5b58\u5728\uff0c\u5373\u76f8\u5bf9\u4e8e\u968f\u673a\u7f51\u7edc\u800c\u8a00\u5c01\u95ed\u4e09\u89d2\u5f62\u7684\u8fc7\u91cf\uff0c\u4e5f\u4ee5\u4e0d\u540c\u65b9\u5f0f\u88ab\u8003\u8651\u3002\u6839\u636e\u805a\u7c7b\u7684\u5b9a\u4e49\u65b9\u5f0f\u4ee5\u53ca\u5176\u503c\u662f\u9ad8\u8fd8\u662f\u4f4e\uff0c\u7f51\u7edc\u53ef\u80fd\u88ab\u8ba4\u4e3a\u6bd4\u5176\u672a\u805a\u7c7b\u7684\u5bf9\u5e94\u7cfb\u7edf\u9c81\u68d2\u6216\u66f4\u4e0d\u9c81\u68d2[105-108]\u3002\u8d85\u8d8a\u5c40\u90e8\u62d3\u6251\u5173\u8054\uff0c\u5c55\u793a\u4ecb\u89c2\u975e\u5e73\u51e1\u7ed3\u6784\u7684\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u662f\u53e6\u4e00\u4e2a\u9002\u5408\u5728\u6e17\u6d41\u6846\u67b6\u4e0b\u5904\u7406\u7684\u73b0\u8c61\u3002\u4e00\u79cd\u53ef\u80fd\u7684\u4ecb\u89c2\u5c3a\u5ea6\u7ed3\u6784\u662f\u6838\u5fc3-\u5916\u56f4\u7f51\u7edc\u7ec4\u7ec7[109]\u3002\u5f53\u8fd9\u4e9b\u7ed3\u6784\u968f\u673a\u53d7\u5230\u653b\u51fb\u65f6\uff0c\u5b83\u4eec\u53ef\u80fd\u8868\u73b0\u51fa\u4e24\u4e2a\u74e6\u89e3\u70b9\uff1a\u4e00\u4e2a\u7531\u6838\u5fc3\u4e2d\u7684\u8282\u70b9\u5f15\u8d77\uff0c\u53e6\u4e00\u4e2a\u7531\u5916\u56f4\u4e2d\u7684\u8282\u70b9\u5f15\u8d77[110-112]\u3002\u53e6\u4e00\u79cd\u7ed3\u6784\u662fk-\u56e2\uff0c\u57fa\u4e8e\u6e17\u6d41\u7684\u5206\u6790\u6709\u52a9\u4e8e\u8bc6\u522b\u5176\u91cd\u53e0\u793e\u56e2[113]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u74e6\u89e3\u53ef\u80fd\u4f1a\u4ee5\u4e00\u79cd\u6781\u96be\u9884\u6d4b\u7684\u7a81\u7136\u65b9\u5f0f\u53d1\u751f\uff0c\u56e0\u4e3a\u7f3a\u4e4f\u660e\u663e\u7684\u9884\u8b66\u4fe1\u53f7\u3002\u8fd9\u7c7b\u7a81\u53d8\u53ef\u80fd\u4f1a\u5bf9\u793e\u4f1a\u7ecf\u6d4e\u4ea7\u751f\u5de8\u5927\u5f71\u54cd\u3002\u6700\u8fd1\u7684\u4f8b\u5b50\u5305\u62ec2008\u5e74\u91d1\u878d\u5371\u673a[114]\u5e26\u6765\u7684\u6df1\u8fdc\u5f71\u54cd\uff0c\u4ee5\u53caCOVID-19\u7684\u4f20\u64ad[115]\u5bfc\u81f4\u5168\u7403\u7ecf\u6d4e\u8870\u9000\u548c\u751f\u6d3b\u6807\u51c6\u7684\u6839\u672c\u6027\u6539\u53d8\u3002\u56e0\u6b64\uff0c\u8bc6\u522b\u53ef\u80fd\u51fa\u73b0\u7a81\u7136\u76f8\u53d8\u7684\u60c5\u666f\u5177\u6709\u91cd\u8981\u4ef7\u503c\u3002\u6e17\u6d41\u7406\u8bba\u63d0\u4f9b\u4e86\u591a\u79cd\u673a\u5236\uff0c\u53ef\u4ee5\u5f15\u53d1\u8fd9\u79cd\u5267\u70c8\u7684\u62d3\u6251\u5206\u88c2\u3002\u5176\u4e2d\u4e00\u79cd\u662f\u6240\u8c13\u7684k-\u6838\u6e17\u6d41\uff0c\u5373\u8fed\u4ee3\u5730\u79fb\u9664\u6240\u6709\u5ea6\u6570\u5c0f\u4e8ek\u7684\u8282\u70b9[116]\u3002\u5bf9\u4e8ek = 2\uff0c\u76f8\u53d8\u662f\u8fde\u7eed\u7684\uff0c\u4f46\u5bf9\u4e8ek > 2\uff0c\u5b83\u53d8\u4e3a\u6df7\u5408\u578b\u3002\u81ea\u4e3e\u6e17\u6d41<\/span> (Bootstap percolation) <\/span>\u4e5f\u53ef\u80fd\u5448\u73b0\u4e0d\u8fde\u7eed\u548c\u6df7\u5408\u578b\u76f8\u53d8\uff0c\u5b83\u5141\u8bb8\u88ab\u79fb\u9664\u7684\u8282\u70b9\u5728\u5176\u90bb\u5c45\u6570\u91cf\u8d85\u8fc7\u4e00\u5b9a\u9608\u503c\u65f6\u6062\u590d[117]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6b64\u5916\uff0c\u8fd8\u6709\u4e00\u7cfb\u5217\u57fa\u4e8e\u7279\u5b9a\u9009\u62e9\u89c4\u5219\u7684\u6a21\u578b\uff0c\u53ef\u80fd\u4f1a\u663e\u8457\u52a0\u901f\u6216\u5ef6\u8fdf\u8fbe\u5230\u4e34\u754c\u70b9\uff0c\u5c3d\u7ba1\u8fd9\u9700\u8981\u4f9d\u8d56\u4e8e\u4ecb\u89c2\u5c42\u9762\u7684\u4fe1\u606f[118-121]\u3002\u5176\u4e2d\u6700\u8457\u540d\u7684\u662f\u5bfc\u81f4\u7206\u70b8\u6e17\u6d41<\/span>\uff08explosive percolation\uff09<\/span>\u7684\u4e58\u79ef\u89c4\u5219[122]\u3002\u4e58\u79ef\u89c4\u5219\u5305\u62ec\u968f\u673a\u5747\u5300\u9009\u62e9\u4e24\u6761\u8fde\u8fb9\uff0c\u5e76\u79fb\u9664\u8fde\u63a5\u7684\u4e24\u4e2a\u7ec4\u5206\u89c4\u6a21\u4e58\u79ef\u6700\u5927\u7684\u8fde\u8fb9\uff1a\u8fd9\u6837\uff0c\u6e17\u6d41\u7684\u5f00\u59cb\u53d8\u5f97\u7a81\u7136\u3002\u6b64\u5916\uff0c\u74e6\u89e3\u70b9\u53d1\u751f\u5728\u57fa\u4e8e\u968f\u673a\u8fde\u8fb9\u9009\u62e9\u7684\u6e17\u6d41\u6848\u4f8b\u4e4b\u524d\u3002\u5c3d\u7ba1\u8fd9\u79cd\u76f8\u53d8\u770b\u8d77\u6765\u7a81\u7136\uff0c\u4f46\u5df2\u7ecf\u8bc1\u660e\uff0c\u4e58\u79ef\u89c4\u5219\u7684\u7206\u70b8\u6027\u8f6c\u53d8\u5b9e\u9645\u4e0a\u662f\u8fde\u7eed\u7684\uff0c\u4f46\u5177\u6709\u72ec\u7279\u7684\u4e34\u754c\u884c\u4e3a[123-125]\u3002\u5173\u4e8e\u7206\u70b8\u6e17\u6d41\u7684\u66f4\u591a\u4fe1\u606f\u53ef\u4ee5\u5728\u6700\u8fd1\u7684\u4e00\u7bc7\u7efc\u8ff0\u4e2d\u627e\u5230[126]\u3002\u6700\u540e\uff0c\u4e0e\u4e0d\u540c\u7f51\u7edc\u8026\u5408\u65f6\u7684\u4e92\u4f9d\u8d56\u6027\u76f8\u5173\u7684\u673a\u5236\u4e5f\u53ef\u80fd\u5bfc\u81f4\u7a81\u7136\u7684\u74e6\u89e3\uff0c\u4e92\u4f9d\u8d56\u6027\u5728\u7814\u7a76\u7ea7\u8054\u5931\u6548\u4e2d\u8d77\u7740\u6838\u5fc3\u4f5c\u7528\uff0c\u5c06\u5728\u4e0b\u4e00\u8282\u4e2d\u8ba8\u8bba\uff0c\u4f46\u5b83\u4eec\u53ef\u4ee5\u7528\u9759\u6001\u6e17\u6d41\u6846\u67b6\u8fdb\u884c\u5efa\u6a21\uff0c\u5e76\u63ed\u793a\u51fa\u4e0d\u8fde\u7eed\u76f8\u53d8\u51fa\u73b0\u7684\u6761\u4ef6[127]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u603b\u4f53\u800c\u8a00\uff0c\u7531\u4e8e\u5176\u7075\u6d3b\u6027\u3001\u4f4e\u8ba1\u7b97\u6210\u672c\u548c\u5f3a\u5927\u7684\u5206\u6790\u80fd\u529b\uff0c\u6e17\u6d41\u7406\u8bba\u5728\u7f51\u7edc\u9c81\u68d2\u6027\u7814\u7a76\u4e2d\u5360\u636e\u4e86\u6838\u5fc3\u5730\u4f4d\u3002\u5b83\u63d0\u51fa\u4e86\u6839\u636e\u67d0\u4e9b\u5ea6\u91cf\u6765\u74e6\u89e3\u4e92\u8fde\u7cfb\u7edf\u7684\u51c6\u5219\uff0c\u4ece\u800c\u63ed\u793a\u4e86\u8fd9\u4e9b\u7cbe\u786e\u6307\u6807\u5bf9\u4e8e\u7cfb\u7edf\u8106\u5f31\u6027\u7684\u91cd\u8981\u6027\u3002\u7136\u800c\uff0c\u5728\u5176\u4ed6\u60c5\u51b5\u4e0b\uff0c\u5e72\u9884\u51c6\u5219\u4e0d\u4f9d\u8d56\u4e8e\u7279\u5b9a\u5ea6\u91cf\u6807\u51c6\uff0c\u800c\u662f\u4ee5\u5b9e\u73b0\u7279\u5b9a\u76ee\u6807\u4e3a\u5bfc\u5411\u3002\u57fa\u4e8e\u8fd9\u4e00\u601d\u8def\uff0c\u6211\u4eec\u5728\u4e0b\u4e00\u8282\u5c06\u91cd\u70b9\u8ba8\u8bba\u65e8\u5728\u5bfb\u627e\u5c3d\u53ef\u80fd\u9ad8\u6548\u5730\u74e6\u89e3\u7f51\u7edc\u7684\u7b56\u7565\u7684\u7b97\u6cd5\u3002<\/span><\/section>\n

    <\/section>\n

    <\/span><\/section>\n

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    <\/section>\n
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    <\/svg><\/section>\n<\/section>\n<\/section>\n
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    \u56db\u3001\u6700\u4f18\u6e17\u6d41\u548c\u7f51\u7edc\u74e6\u89e3<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


    <\/p>\n

    \u5bfb\u627e\u6700\u4f18\u7b56\u7565\uff0c\u5373\u627e\u51fa\u5b9e\u73b0\u7f51\u7edc\u6700\u5feb\u74e6\u89e3\u7684\u6700\u5c0f\u8282\u70b9\u96c6\u5408\uff0c\u662f\u6700\u4f18\u6e17\u6d41\u95ee\u9898<\/span>\uff08Optimal percolation\uff09<\/span>[128]\uff0c\u4e5f\u88ab\u79f0\u4e3a\u7f51\u7edc\u74e6\u89e3<\/span>\uff08network dismantling\uff09<\/span>[69]\u3002\u8fd9\u662f\u4e00\u4e2a\u7ec4\u5408\u4f18\u5316\u95ee\u9898\uff0c\u65e8\u5728\u5bfb\u627e\u79fb\u9664\u65f6\u80fd\u6700\u5feb\u7834\u574f\u7f51\u7edc\u7684\u8282\u70b9<\/span>\uff08\u6216\u8fde\u8fb9\uff09<\/span>\u96c6\u5408\uff0c\u4f7f\u6700\u5927\u8fde\u901a\u7247\u5206\u89e3\u4e3a\u5b64\u7acb\u7684\u5b50\u7ec4\u4ef6\uff0c\u4ece\u800c\u6709\u6548\u964d\u4f4e\u7cfb\u7edf\u7684\u529f\u80fd\u3002\u5373\u4fbf\u5728\u5c0f\u578b\u7f51\u7edc\u4e0a\uff0c\u8fd9\u6837\u7684\u4f18\u5316\u95ee\u9898\u5728\u8ba1\u7b97\u4e0a\u4e5f\u662f\u5177\u6709\u6311\u6218\u6027\u7684<\/span>\uff08\u5373\uff0c\u5b83\u662fNP-hard\u96be\u9898\uff09<\/span>\uff0c\u800c\u4e14\u5173\u4e8e\u74e6\u89e3\u8fc7\u7a0b\u540e\u5b50\u7ec4\u4ef6\u5e94\u6709\u7684\u5927\u5c0f\uff0c\u751a\u81f3\u662f\u74e6\u89e3\u7684\u76ee\u6807\u5728\u6587\u732e\u4e2d\u6ca1\u6709\u7edf\u4e00\u610f\u89c1\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u65e9\u671f\u7684\u5de5\u4f5c\u81f4\u529b\u4e8e\u901a\u8fc7\u8bc4\u4f30\u8282\u70b9\u7684\u4e00\u7cfb\u5217\u62d3\u6251\u4e2d\u5fc3\u6027\u6765\u627e\u5230\u7834\u574f\u7f51\u7edc\u7684\u6700\u5c0f\u8282\u70b9\u96c6\u3002\u7834\u574f\u7f51\u7edc\u7684\u4e00\u4e2a\u7b80\u5355\u7b56\u7565\u662f\u6309\u7167\u4e2d\u5fc3\u6027\u8bc4\u5206\u7684\u987a\u5e8f\u653b\u51fb\u8282\u70b9\u3002\u6700\u57fa\u672c\u7684\u8bc4\u5206\u65b9\u6cd5\u662f\u8282\u70b9\u7684\u5ea6\u503c\uff0c\u8fd9\u79cd\u65b9\u6cd5\u57fa\u4e8e\u201c\u8fde\u63a5\u8d8a\u591a\u8d8a\u597d\u201d\u7684\u76f4\u89c9\u504f\u597d\u4e8e\u67a2\u7ebd\u8282\u70b9[29,73]\u3002\u8fd9\u4e9b\u7b56\u7565\u4e5f\u53ef\u4ee5\u5206\u4e3a\u9759\u6001\u548c\u52a8\u6001\u4e24\u79cd\uff0c\u524d\u8005\u5728\u74e6\u89e3\u8fc7\u7a0b\u5f00\u59cb\u65f6\u8ba1\u7b97\u8282\u70b9<\/span>\uff08\u6216\u8fde\u8fb9\uff09<\/span>\u7684\u79fb\u9664\u6392\u5e8f\uff0c\u800c\u540e\u8005\u5219\u5728\u8fc7\u7a0b\u4e2d\u66f4\u65b0\u6392\u5e8f\uff0c\u4ece\u800c\u80fd\u591f\u9002\u5e94\u7f51\u7edc\u72b6\u6001\u7684\u53d8\u5316\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7136\u800c\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u5173\u952e\u8282\u70b9\u5e76\u975e\u8fde\u63a5\u6700\u591a\u7684\u8282\u70b9\uff0c\u800c\u662f\u90a3\u4e9b\u8fde\u63a5\u8f83\u5c11\u4f46\u5728\u7f51\u7edc\u6838\u5fc3\u5360\u636e\u6218\u7565\u4f4d\u7f6e\u7684\u8282\u70b9\u3002\u8fd9\u4e9b\u62d3\u6251\u6865\u6881\u4f53\u73b0\u4e86\u793e\u4f1a\u5b66\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u6982\u5ff5\uff0c\u5373\u201c\u5f31\u94fe\u63a5\u7684\u529b\u91cf\u201d[129]\u3002\u4e3a\u4e86\u627e\u5230\u8fd9\u4e9b\u5173\u952e\u8282\u70b9\uff0c\u5df2\u7ecf\u63d0\u51fa\u4e86\u8bb8\u591a\u542f\u53d1\u5f0f\u7684\u4e2d\u5fc3\u6027\u5ea6\u91cf\u6807\u51c6\u3002\u5b83\u4eec\u53ef\u4ee5\u5927\u81f4\u5206\u4e3a\u4ee5\u4e0b\u51e0\u7c7b\uff1a\u57fa\u4e8e\u5ea6\u503c\u7684<\/span>\uff08\u5982\u67a2\u7ebd\u548ck-\u6838\uff09<\/span>\u3001\u57fa\u4e8e\u6700\u77ed\u8def\u5f84\u7684<\/span>\uff08\u5982\u63a5\u8fd1\u4e2d\u5fc3\u6027\u548c\u4ecb\u6570\u4e2d\u5fc3\u6027\uff09<\/span>\u3001\u57fa\u4e8e\u8def\u5f84\u7684<\/span>\uff08\u5982\u7279\u5f81\u5411\u91cf\u3001\u7279\u5f81\u503c\u548cKatz\u4e2d\u5fc3\u6027\uff09<\/span>\u3001\u57fa\u4e8e\u968f\u673a\u6e38\u8d70\u7684<\/span>\uff08\u5982PageRank\uff09<\/span>\u3001\u57fa\u4e8e\u975e\u56de\u6eaf\u6e38\u8d70\u7684\uff0c\u4ee5\u53ca\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u65b9\u6cd5\u3002\u66f4\u9ad8\u5c42\u6b21\u7684\u5206\u7c7b\u4e2d\uff0c\u53ef\u4ee5\u533a\u5206\u51fa\u771f\u6b63\u57fa\u4e8e\u62d3\u6251\u63cf\u8ff0\u7b26\u7684\u7ed3\u6784\u6027\u65b9\u6cd5\uff0c\u548c\u57fa\u4e8e\u8282\u70b9\u95f4\u67d0\u79cd\u6d41\u52a8\u52a8\u529b\u5b66\u7684\u65b9\u6cd5\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6700\u4f18\u6e17\u6d41\u5c06\u5bfb\u627e\u6700\u4f18\u8282\u70b9\u653b\u51fb\u96c6\u7684\u641c\u7d22\u8fc7\u7a0b\u7cfb\u7edf\u5316\uff0c\u8bd5\u56fe\u627e\u5230\u4e00\u7ec4\u8282\u70b9\u914d\u7f6en*\uff0c\u5bf9\u5e94\u4e8e\u6700\u5c0f\u7684\u79fb\u9664\u6bd4\u4f8b<\/sub><\/span>\uff0c\u4f7f\u5f97\u7f51\u7edcG\u221e<\/sub>\u7684\u6700\u5927\u8fde\u901a\u5206\u91cf\u88ab\u6700\u4f18\u5730\u74e6\u89e3[128]\uff1a<\/span><\/section>\n

    <\/section>\n

    <\/section>\n

    <\/section>\n
    \u6700\u4f18\u6e17\u6d41\u662f\u4e00\u4e2aNP-hard\u7684\u7ec4\u5408\u4f18\u5316\u95ee\u9898[130]\uff0c\u7531\u4e8e\u65e0\u6cd5\u5b9e\u73b0G<\/span>\u221e<\/sub>(n)\u7684\u663e\u5f0f\u51fd\u6570\u5f62\u5f0f\uff0c\u4f7f\u5f97\u8fd9\u4e2a\u95ee\u9898\u96be\u4ee5\u76f4\u63a5\u89e3\u51b3\u3002\u7136\u800c\uff0c\u5bf9\u7a00\u758f\u7f51\u7edc[128]\uff0c\u5b58\u5728\u4e00\u4e2a\u8fd1\u4f3c\u89e3\u65b9\u6848\uff0c\u4ece\u800c\u5f15\u51fa\u4e86\u96c6\u4f53\u5f71\u54cd\u529b<\/span>\uff08collective influence, CI\uff09<\/span>\u7b97\u6cd5[131]\u3002\u4e00\u4e2a\u8fd1\u4f3c\u6700\u4f18\u96c6\u5408\u53ef\u4ee5\u88ab\u89c6\u4e3a\u4e00\u7cfb\u5217\u4f18\u5316\u653b\u51fb\u7684<\/span>\uff08\u65e0\u9650\uff09<\/span>\u5e8f\u5217\uff0c\u8fd9\u4e9b\u653b\u51fb\u662f\u5bf9\u975e\u56de\u6eaf\u77e9\u9635\u6700\u5927\u7279\u5f81\u503c\u6700\u5c0f\u5316\u7684\u8fde\u7eed\u903c\u8fd1\u3002\u8fd9\u5c31\u4ea7\u751f\u4e86\u5177\u6709\u5ea6\u503cki<\/sub>\u7684\u8282\u70b9i\u7684CI\u6307\u6570\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/section>\n
    \u5176\u4e2d\uff0c<\/sub><\/span>\u8868\u793a\u4ee5\u8282\u70b9i\u4e3a\u4e2d\u5fc3\u3001\u534a\u5f84\u4e3a<\/sub><\/span><\/span>\uff08\u57fa\u4e8e\u6700\u77ed\u8def\u5f84\u8ddd\u79bb\u4f30\u7b97\uff09<\/span>\u7684\u7403\u4f53\u8868\u9762\u3002\u8fd9\u4e2a\u7b97\u6cd5\u63d0\u4f9b\u4e86\u5bf9\u6700\u4f18\u6e17\u6d41\u96c6\u7684\u826f\u597d\u8fd1\u4f3c\u3002\u540e\u6765\uff0c\u57fa\u4e8e\u6d88\u606f\u4f20\u9012[132]\u548c\u7f6e\u4fe1\u5ea6\u4f20\u64ad<\/span>\uff08belief propagation\uff09<\/span>[133]\u7684\u66f4\u597d\u7b97\u6cd5\u88ab\u63d0\u51fa\uff0c\u5305\u62ec\u53bb\u73af\u74e6\u89e3[69,134]\u4ee5\u53ca\u7206\u70b8\u6e17\u6d41[64]\u3002\u8fd9\u4e9b\u65b9\u6cd5\u4e25\u8c28\u5730\u5904\u7406\u4e86\u6700\u4f18\u6e17\u6d41\u95ee\u9898\uff0c\u589e\u8fdb\u4e86\u6211\u4eec\u7684\u7406\u89e3\uff0c\u5e76\u8fdb\u4e00\u6b65\u4ea7\u751f\u4e86\u4e00\u7cfb\u5217\u9002\u7528\u4e8e\u5927\u89c4\u6a21\u590d\u6742\u7cfb\u7edf\u590d\u6742\u800c\u9ad8\u6548\u7684\u7b97\u6cd5\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e00\u9879\u7814\u7a76\u8868\u660e[134]\uff0c\u901a\u8fc7\u7834\u574f\u7531\u6700\u5c0f\u53cd\u9988\u8282\u70b9\u96c6\u627e\u5230\u7684\u5faa\u73af<\/span>\uff08\u4e5f\u79f0\u4e3a\u201c\u53bb\u73af\u201d\uff09<\/span>\u53ef\u4ee5\u5b9e\u73b0\u6700\u5927\u8fde\u901a\u7247\u7684\u6700\u4f18\u74e6\u89e3\u3002\u5bf9\u4e8e\u7a00\u758f\u968f\u673a\u7f51\u7edc\uff0c\u5c0f\u8fde\u901a\u5206\u91cf\u4e2d\u5f88\u5c11\u5b58\u5728\u77ed\u73af\u3002\u5982\u679c\u5207\u65ad\u6700\u5927\u8fde\u901a\u7247\u4e2d\u7684\u957f\u73af\uff0c\u7f51\u7edc\u5c06\u5206\u88c2\u6210\u5c0f\u7684\u6811\u72b6\u7247\u6bb5\u3002\u6700\u4f18\u53bb\u73af\u9608\u503c<\/sub><\/span>\u5bf9\u5e94\u6700\u4f18\u6e17\u6d41\u9608\u503c<\/sub><\/span>\u7684\u4e0a\u9650[69]\u3002\u6700\u4f18\u53bb\u73af\u662f\u4e00\u4e2aNP-hard\u95ee\u9898\uff0c\u53ef\u4ee5\u901a\u8fc7\u7f6e\u4fe1\u5ea6\u4f20\u64ad\u7b97\u6cd5\u8fd1\u4f3c\u6c42\u89e3\u3002\u5df2\u7ecf\u5f00\u53d1\u4e86\u4e24\u79cd\u65b9\u6cd5\uff1a\u7f6e\u4fe1\u5ea6\u4f20\u64ad\u5f15\u5bfc\u7684\u5316\u7b80\u7b97\u6cd5<\/span>\uff08the belief propagation-guided decimation algorithm\uff09<\/span> [134]\u548cMin-Sum\u7b97\u6cd5[69] \uff0c\u5c3d\u7ba1\u590d\u6742\u5ea6\u6709\u6240\u589e\u52a0\uff0c\u5b83\u4eec\u627e\u5230\u7684\u5f71\u54cd\u529b\u8282\u70b9\u96c6\u5408\u6bd4CI\u7b97\u6cd5\u66f4\u5c0f\u3002\u7279\u522b\u662f\uff0c\u8fd9\u4e24\u79cd\u7b97\u6cd5\u9996\u5148\u901a\u8fc7\u6d88\u606f\u4f20\u9012\u7b97\u6cd5\u5bf9\u7f51\u7edc\u8fdb\u884c\u53bb\u73af\u5904\u7406\uff0c\u7136\u540e\u4f7f\u7528\u6811\u7834\u574f\u5668\u7b97\u6cd5<\/span>\uff08tree-breaker algorithm\uff09<\/span>\u5206\u89e3\u6240\u5f97\u5230\u7684\u68ee\u6797<\/span>\uff08\u5373\u6811\u7684\u4e0d\u76f8\u4ea4\u7ec4\u5408\uff09<\/span>\u3002\u5c3d\u7ba1\u6d88\u606f\u4f20\u9012\u8fed\u4ee3\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u4e0e\u8fde\u8fb9\u6570\u5448\u7ebf\u6027\u5173\u7cfb\uff0c\u4f46\u53c2\u8003\u6587\u732e[69]\u4e2d\u63d0\u51fa\u7684\u8d2a\u5a6a\u6811\u7834\u574f\u5668\u7b97\u6cd5\u7684\u590d\u6742\u5ea6O(N(log(N+T)))\u968fT\u548cN\u6570\u91cf\u7ea7\u7f29\u653e\uff0c\u5176\u4e2dT\u662f\u68ee\u6797\u4e2d\u6811\u7684\u6700\u5927\u76f4\u5f84\uff0cN\u662f\u8282\u70b9\u6570\u3002\u6b64\u5916\uff0cMin-Sum\u7b97\u6cd5\u8fd8\u5305\u62ec\u653b\u51fb\u7ed3\u675f\u540e\u7684\u91cd\u65b0\u63d2\u5165\u9636\u6bb5\uff0c\u5373\u4e00\u4e2a\u8d2a\u5a6a\u8fc7\u7a0b\uff0c\u91cd\u65b0\u63d2\u5165\u5b9e\u9645\u4e0a\u4e0d\u9700\u8981\u7684\u8282\u70b9\u4ee5\u8fbe\u5230\u9884\u671f\u76ee\u6807\u3002\u8fd9\u4e2a\u91cd\u63d2\u5165\u9636\u6bb5\u65e8\u5728\u51cf\u5c11\u5b9e\u9645\u4ece\u7f51\u7edc\u4e2d\u79fb\u9664\u7684\u8282\u70b9\u6570\uff0c\u4ece\u800c\u964d\u4f4e\u653b\u51fb\u6210\u672c\uff0c\u9002\u7528\u4e8e\u80d6\u5c3e\u7f51\u7edc\uff0c\u5728\u8fd9\u4e9b\u7f51\u7edc\u4e2d\uff0c\u53bb\u73af\u548c\u74e6\u89e3\u95ee\u9898\u5e76\u4e0d\u7b49\u540c\u3002\u8fd9\u4e00\u9636\u6bb5\u62a5\u544a\u4e3a\u4e9a\u7ebf\u6027\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u4f46\u786e\u5207\u7684\u590d\u6742\u6027\u5c1a\u672a\u660e\u786e[135]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u53d7\u5230\u8fd9\u4e9b\u57fa\u4e8e\u53bb\u73af\u7684\u7b97\u6cd5\u7684\u542f\u53d1\uff0c\u7814\u7a76\u8005\u4eec\u5f00\u53d1\u4e86\u5176\u4ed6\u7b97\u6cd5\u3002CoreHD[135]\u662f\u4e00\u4e2a\u7b80\u5355\u800c\u5feb\u901f\u7684\u542f\u53d1\u5f0f\u7b97\u6cd5\uff0c\u5bf9\u4e8e\u7a00\u758f\u7f51\u7edc\u5176\u590d\u6742\u5ea6\u4e3aO(N)\uff0c\u5176\u601d\u60f3\u662f\u901a\u8fc7\u8fed\u4ee3\u4ece2-\u6838\u4e2d\u79fb\u9664\u5ea6\u503c\u6700\u9ad8\u7684\u8282\u70b9\u6765\u5b9e\u73b0\u53bb\u73af\uff0c\u7136\u540e\u91c7\u7528\u4e0eMin-Sum\u7b97\u6cd5\u76f8\u540c\u7684\u6811\u7834\u574f\u548c\u91cd\u63d2\u5165\u7b97\u6cd5\u3002\u7206\u70b8\u6027\u514d\u75ab\u7b97\u6cd5[64]\u57fa\u4e8e\u7206\u70b8\u6e17\u6d41\u76f8\u53d8\u3002\u5e7f\u4e49\u7f51\u7edc\u74e6\u89e3[66,136]\u65e8\u5728\u89e3\u51b3\u975e\u5355\u5143\u7684\u79fb\u9664\u6210\u672c\u95ee\u9898\uff0c\u5e76\u57fa\u4e8e\u8fed\u4ee3\u79fb\u9664\u90a3\u4e9b\u80fd\u6700\u5927\u5316\u8fd1\u4f3c\u8c31\u5206\u5272\u7684\u8282\u70b9\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5176\u4ed6\u7814\u7a76\u8fd8\u63d0\u51fa\u4e86\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u653b\u51fb\u7b56\u7565\uff0c\u5982\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u56fe\u74e6\u89e3<\/span>\uff08graph dismantling with machine learning , GDM\uff09<\/span>[68]\u548cFINDER[137]\u3002\u8fd9\u4e24\u79cd\u65b9\u6cd5\u90fd\u5229\u7528\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\uff0c\u5177\u4f53\u6765\u8bf4\u662f\u56fe\u795e\u7ecf\u7f51\u7edc\uff0c\u5728\u5c0f\u578b\u5408\u6210\u7f51\u7edc\u4e0a\u5b66\u4e60\u653b\u51fb\u7b56\u7565\u3002\u7136\u800c\uff0cGDM\u662f\u5728\u66b4\u529b\u6c42\u89e3\u51fa\u7684\u7f51\u7edc\u6700\u4f18\u74e6\u89e3\u8282\u70b9\u96c6\u5408\u6570\u636e\u4e0a\u8fdb\u884c\u76d1\u7763\u5b66\u4e60\uff0c\u800cFINDER\u91c7\u7528\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5\u3002\u53e6\u4e00\u4e2a\u7b97\u6cd5\u662fCoreGDM[138]\uff0c\u5b83\u53d7\u5230CoreHD\u7684\u542f\u53d1\uff0c\u4f7f\u7528GDM\u6a21\u578b\u653b\u51fb\u7f51\u7edc\u76842-\u6838\u3002\u6b64\u5916\uff0c\u8fd8\u7814\u7a76\u4e86\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u548c\u53cc\u66f2\u7a7a\u95f4\u4e2d\u7f51\u7edc\u5d4c\u5165\u7684\u6027\u80fd[139]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
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    <\/span><\/section>\n
    \u5728\u7f51\u7edc\u52a8\u529b\u5b66\u4fe1\u606f\u6d41\u65b9\u9762\uff0c\u6700\u4f18\u6e17\u6d41\u65e8\u5728\u5bfb\u627e\u80fd\u963b\u6b62\u4fe1\u606f\u4f20\u64ad\u7684\u201c\u8d85\u7ea7\u963b\u65ad\u8005\u201d\u7684\u6700\u5c0f\u96c6\u5408 [142]\u3002\u4e00\u4e2a\u76f8\u5bf9\u7684\u95ee\u9898\u662f\u627e\u5230\u80fd\u5728\u88ab\u9009\u4e3a\u79cd\u5b50\u65f6\u6700\u5927\u5316\u4fe1\u606f\u4f20\u64ad\u7684\u8d85\u7ea7\u4f20\u64ad\u8005\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u8fd9\u4e24\u4e2a\u95ee\u9898\u5e76\u4e0d\u4e00\u5b9a\u7b49\u4ef7[143]\u3002\u7136\u800c\uff0c\u5728\u4e00\u79cd\u7279\u5b9a\u5f62\u5f0f\u7684\u7ebf\u6027\u9608\u503c\u4f20\u64ad\u6a21\u578b\u4e2d\uff0c\u9608\u503c\u7531\u7ed9\u51fa\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6700\u4f18\u6e17\u6d41\u4e0e\u5f71\u54cd\u529b\u6700\u5927\u5316\u95ee\u9898\u7b49\u4ef7[128,130]\u3002\u5f71\u54cd\u529b\u6700\u5927\u5316\u95ee\u9898\u7684\u76ee\u6807\u662f\u627e\u5230\u80fd\u5728\u7f51\u7edc\u4e2d\u5f15\u53d1\u6700\u5927\u89c4\u6a21\u4fe1\u606f\u4f20\u64ad\u8fc7\u7a0b\u7684k<\/em>\u4e2a\u8d85\u7ea7\u4f20\u64ad\u8005<\/span>\uff08\u5f71\u54cd\u8005\uff09<\/span>\u7684\u6700\u4f18\u96c6\u5408\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u6570\u91cf\u7684\u521d\u59cb\u4f20\u64ad\u8005k<\/em>\uff0c\u6211\u4eec\u5e0c\u671b\u627e\u5230\u4e00\u4e2a\u5177\u6709\u6700\u5927\u5f71\u54cd\u529b\u03c3(S*) \u7684k<\/em>\u8282\u70b9\u96c6\u5408S*\uff1a<\/span><\/section>\n

    <\/section>\n
    <\/section>\n

    <\/section>\n
    \u8fd9\u79cd\u65b9\u6cd5\u5c06\u6700\u4f18\u6e17\u6d41\u7684\u5e94\u7528\u6269\u5c55\u5230\u4e86\u5404\u79cd\u793e\u4f1a\u95ee\u9898\u548c\u66f4\u5e7f\u6cdb\u7684\u9886\u57df\uff1a\u5f71\u54cd\u8005\u7406\u8bba\u5728\u591a\u4e2a\u5e94\u7528\u4e2d\u53d1\u6325\u4f5c\u7528\uff0c\u6bd4\u5982\u5728\u793e\u4ea4\u5a92\u4f53\u4e2d\u8bc6\u522b\u6709\u5f71\u54cd\u529b\u7684\u4f20\u64ad\u8005\u3001\u5728\u5927\u6d41\u884c\u75c5\u4e2d\u627e\u51fa\u8d85\u7ea7\u4f20\u64ad\u8005\u3001\u8bc6\u522b\u53ef\u80fd\u5bfc\u81f4\u75be\u75c5\u7684\u9057\u4f20\u7f51\u7edc\u4e2d\u7684\u5173\u952e\u57fa\u56e0\u7a81\u53d8\u3001\u786e\u5b9a\u5927\u8111\u4e2d\u5bf9\u6574\u5408\u81f3\u5173\u91cd\u8981\u7684\u533a\u57df\u3001\u8bc6\u522b\u5176\u706d\u7edd\u53ef\u80fd\u5f15\u53d1\u751f\u6001\u7cfb\u7edf\u5d29\u6e83\u7684\u5173\u952e\u7269\u79cd\uff0c\u4ee5\u53ca\u5bfb\u627e\u201c\u5927\u5230\u4e0d\u80fd\u5931\u8d25\u201d<\/span>\uff08too big to fail\uff09<\/span>\u7684\u91d1\u878d\u673a\u6784\u3002<\/span><\/section>\n

    <\/span><\/section>\n
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    <\/span><\/section>\n
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    <\/span><\/section>\n
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    <\/span><\/p>\n

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    <\/span><\/section>\n
    <\/section>\n

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    <\/section>\n
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    <\/section>\n

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    <\/span><\/section>\n
    \u9664\u4e86\u88681\u4e2d\u5c55\u793a\u7684\u7279\u8bbe\u7b97\u6cd5\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u91c7\u7528\u76f4\u63a5\u4f18\u5316\u7b97\u6cd5<\/span>\uff08\u5982\u6a21\u62df\u9000\u706b\u3001\u7981\u5fcc\u641c\u7d22\u6216\u9057\u4f20\u7b97\u6cd5\uff09<\/span>\u6765\u5bfb\u627e\u6700\u4f18\u7684\u74e6\u89e3\u96c6\u5408qc<\/sub>\u3002\u7136\u800c\uff0c\u7531\u4e8e\u641c\u7d22\u7a7a\u95f4\u7ef4\u5ea6\u5927\uff0c\u8fd9\u4e9b\u7b97\u6cd5\u7684\u6269\u5c55\u6027\u5e76\u4e0d\u597d\uff0c\u56e0\u6b64\u5f80\u5f80\u65e0\u6cd5\u63d0\u4f9b\u6ee1\u610f\u7684\u89e3\u51b3\u65b9\u6848\u3002\u4e3e\u4f8b\u6765\u8bf4\uff0cMin-Sum\u7b97\u6cd5\u7684\u8868\u73b0\u5c31\u8d85\u8fc7\u4e86\u6a21\u62df\u9000\u706b[135]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
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    \u4e94\u3001\u7ea7\u8054\u5931\u6548<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


    <\/p>\n

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    <\/span><\/section>\n
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    <\/span><\/section>\n
    \u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u501f\u52a9\u98ce\u683c\u5316\u6a21\u578b\u6765\u63a2\u8ba8\u4e0d\u540c\u7684\u7ea7\u8054\u5931\u6548\u65b9\u5f0f\uff0c\u8fd9\u4e9b\u6a21\u578b\u65e8\u5728\u63d0\u4f9b\u5bf9\u6545\u969c<\/span>\uff08\u6216\u5176\u4ed6\u4e8b\u7269\uff09<\/span>\u4f20\u64ad\u7684\u666e\u904d\u6d1e\u89c1\u3002\u6211\u4eec\u4ece\u7edf\u8ba1\u7269\u7406\u7684\u89c6\u89d2\u51fa\u53d1\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5ffd\u7565\u4e86\u53ef\u80fd\u8d85\u51fa\u672c\u6587\u8ba8\u8bba\u8303\u56f4\u7684\u7279\u5b9a\u7cfb\u7edf\u7684\u5fae\u89c2\u3001\u9886\u57df\u5bfc\u5411\u7684\u7279\u6027\u3002\u76f8\u53cd\uff0c\u6211\u4eec\u4e3b\u5f20\u5e94\u5c06\u6ce8\u610f\u529b\u96c6\u4e2d\u5728\u5927\u5c3a\u5ea6\u6a21\u5f0f\u548c\u4f17\u591a\u770b\u4f3c\u4e0d\u540c\u7684\u7f51\u7edc\u7cfb\u7edf\u4e2d\u5e38\u89c1\u7684\u96c6\u4f53\u6d8c\u73b0\u884c\u4e3a\u4e0a\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5176\u4e2d\u4e00\u6a21\u578b\u5927\u7c7b\u662f\u90a3\u4e9b\u901a\u8fc7\u76f8\u4e92\u4f9d\u8d56\u5173\u7cfb\u4f20\u64ad\u6545\u969c\u7684\u6a21\u578b\u3002\u8fd9\u662f\u7cfb\u7edf\u7406\u8bba\u4e2d\u7684\u4e00\u4e2a\u6838\u5fc3\u6982\u5ff5\uff0c\u6307\u7684\u662f\u5b8f\u89c2\u7cfb\u7edf\u7684\u4e0d\u540c\u5fae\u89c2\u548c\u4ecb\u89c2\u90e8\u5206\u4e4b\u95f4\u5b58\u5728\u7684\u4f9d\u8d56\u5173\u7cfb\uff0c\u8fd9\u4e9b\u5173\u7cfb\u652f\u6301\u6574\u4e2a\u7cfb\u7edf\u7684\u6b63\u5e38\u529f\u80fd\u3002\u4ece\u751f\u7269\u5316\u5b66\u5230\u4eba\u9020\u884c\u661f\u5de5\u7a0b\u7cfb\u7edf\uff0c\u8fd9\u4e9b\u4f8b\u5b50\u904d\u5e03\u8bb8\u591a\u79d1\u5b66\u5206\u652f[149]\u3002\u4e24\u4e2a\u7b49\u6548\u7684\u7406\u8bba\u6846\u67b6\uff0c\u5373\u591a\u5c42\u7f51\u7edc[21,22,150-152]\u548c\u7f51\u7edc\u7684\u7f51\u7edc[153,154]\uff0c\u5df2\u6210\u529f\u7528\u4e8e\u6784\u5efa\u8fd9\u7c7b\u7ea7\u8054\u7684\u6a21\u578b\u3002\u5728\u8fd9\u4e9b\u6a21\u578b\u4e2d\uff0c\u6bcf\u4e00\u5c42<\/span>\uff08\u6216\u7f51\u7edc\uff09<\/span>\u4e0e\u4e00\u4e2a\u5b50\u7cfb\u7edf\u76f8\u5173\u8054\uff0c\u800c\u4f9d\u8d56\u5173\u7cfb\u5219\u901a\u8fc7\u5c42\u95f4<\/span>\uff08\u6216\u7f51\u7edc\u95f4\uff09<\/span>\u8fde\u8fb9\u7f16\u7801\u3002\u4e0e\u9759\u6001\u6e17\u6d41\u4e0d\u540c\u7684\u662f\uff0c\u8fd9\u79cd\u60c5\u51b5\u6d89\u53ca\u5230\u4e00\u4e2a\u9010\u6b65\u9000\u5316\u7684\u7f51\u7edc\u7684\u5feb\u7167\uff0c\u5176\u74e6\u89e3\u7531\u4f9d\u8d56\u76f8\u5173\u89c4\u5219\u6307\u5bfc<\/span>\uff08\u89c1\u56fe3c\uff09<\/span>\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    2003\u5e74\uff0c\u610f\u5927\u5229\u7535\u7f51\u56e0\u4e00\u5ea7\u7535\u7ad9\u635f\u574f\u800c\u53d1\u751f\u5927\u505c\u7535\uff0c\u5bfc\u81f4\u4e00\u4e9b\u4e92\u8054\u7f51\u901a\u4fe1\u7f51\u7edc\u6545\u969c\uff0c\u8fdb\u800c\u5728\u4e24\u4e2a\u7cfb\u7edf\u95f4\u5f62\u6210\u4e86\u6545\u969c\u7684\u6b63\u5411\u53cd\u9988\u5faa\u73af\u3002\u8fd9\u4e00\u4e8b\u4ef6\u542f\u53d1\u4e86\u4e00\u4e2a\u7406\u8bba\u6a21\u578b\uff0c\u7528\u4e8e\u7814\u7a76\u53cc\u5c42\u7f51\u7edc\u4e2d\u7531\u76f8\u4e92\u4f9d\u8d56\u6027\u5f15\u53d1\u7684\u7ea7\u8054\u5931\u6548[17]\u3002\u6e17\u6d41\u91cf\uff0c\u5982\u6700\u5927\u8054\u901a\u7247\u7684\u5927\u5c0f\uff0c\u53ef\u4ee5\u5728\u6839\u636e\u8be5\u6a21\u578b\u6f14\u53d8\u7684\u7cfb\u7edf\u7684\u6bcf\u4e2a\u5feb\u7167\u4e2d\u8fdb\u884c\u89e3\u6790\u8ddf\u8e2a\uff0c\u4e0e\u6a21\u62df\u7ed3\u679c\u975e\u5e38\u543b\u5408<\/span>\uff08\u89c1\u56fe3d\uff09<\/span>\u3002\u8be5\u7406\u8bba\u7075\u6d3b\u4e14\u53ef\u63a8\u5e7f\u5230\u4efb\u610f\u6570\u91cf\u7684\u8026\u5408\u5b50\u7cfb\u7edf[19,155]\u3001\u90e8\u5206\u548c\u975e\u5bf9\u79f0\u7684\u76f8\u4e92\u4f9d\u8d56\u5173\u7cfb[156,157]\u7b49\u3002\u4f8b\u5982\uff0c\u5982\u679c\u5c42i=1,\u2026,n\u906d\u53d7\u5931\u6548\u6216\u653b\u51fb\uff0c\u5bfc\u81f4\u03a6<\/span>i<\/sub><\/span>\u7684\u529f\u80fd\u8282\u70b9\u6bd4\u4f8b\u4e0b\u964d\uff0c\u800cqji<\/sub>\u8868\u793a\u5c42i\u4e2d\u76f4\u63a5\u4f9d\u8d56\u4e8e\u5c42j\u8282\u70b9\u7684\u8282\u70b9\u6bd4\u4f8b\uff0c\u90a3\u4e48\u5c42\u4e2d\u6700\u5927\u8fde\u901a\u7247\u7684\u7a33\u6001\u503c<\/sub><\/span>\uff0c\u53ef\u4ee5\u901a\u8fc7\u6c42\u89e3\u4ee5\u4e0b\u65b9\u7a0b\u7ec4\u5f97\u5230<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

    <\/section>\n

    <\/p>\n


    <\/section>\n
    \u5176\u4e2d\uff0c<\/sub><\/span>\uff0cfi<\/sub>(Z)=Hi<\/sub>(Zf<\/span>i<\/sub>(Z<\/span>)<\/span>+1-Z)\u3002<\/sub><\/span>\u662f\u5b50\u7cfb\u7edfi\u7684\u5ea6\u751f\u6210\u51fd\u6570\uff0c<\/sub><\/span>\u662f\u5b50\u7cfb\u7edfi\u7684\u5269\u4f59\u5ea6\u751f\u6210\u51fd\u6570\uff0c\u8be5\u5b50\u7cfb\u7edf\u5177\u6709\u5ea6\u5206\u5e03<\/sub><\/span>\u3002K\u662f\u901a\u8fc7\u4f9d\u8d56\u5173\u7cfb\u8fde\u63a5\u5230i\u7684\u5c42\u7684\u6570\u91cf[158]\u3002\u4e5f\u53ef\u4ee5\u5bf9\u7531\u8fde\u8fb9\u6545\u969c\u9a71\u52a8\u7684\u7ea7\u8054\u8fdb\u884c\u5206\u6790\u5904\u7406\uff0c\u4f46\u4e0e\u8282\u70b9\u6545\u969c\u4f20\u64ad\u673a\u5236\u76f8\u6bd4\u7814\u7a76\u7684\u8f83\u5c11\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u516c\u5f0f\uff089\uff09\u81f3\uff0811\uff09\u9884\u6d4b\u4e86\u4e00\u7cfb\u5217\u4e30\u5bcc\u591a\u5f69\u7684\u73b0\u8c61\uff0c\u7136\u800c\u8fd9\u4e9b\u73b0\u8c61\u5bf9\u76f8\u4e92\u4f9d\u8d56\u7cfb\u7edf\u7684\u9c81\u68d2\u6027\u4ea7\u751f\u4e86\u663e\u8457\u5f71\u54cd\u3002\u6700\u663e\u8457\u7684\u73b0\u8c61\u662f\uff0c\u968f\u7740\u7f51\u7edc\u62d3\u6251\u53c2\u6570\u7684\u53d8\u5316\uff0c\u7ea7\u8054\u8fc7\u7a0b\u7ed3\u675f\u65f6\u6700\u5927\u8054\u901a\u7247\u7ecf\u5386\u4e86\u4e00\u4e2a\u4e0d\u8fde\u7eed\u7684\u76f8\u53d8\u3002\u8fd9\u79cd\u7a81\u53d8\u5bfc\u81f4\u7cfb\u7edf\u7684\u7a81\u7136\u5d29\u6e83\uff0c\u800c\u968f\u7740\u5b8c\u5168\u8026\u5408\u5b50\u7cfb\u7edf\u7684\u6570\u91cf\u589e\u52a0\uff0c\u8fd9\u79cd\u5d29\u6e83\u53d8\u5f97\u66f4\u52a0\u96be\u4ee5\u9884\u6d4b<\/span>\uff08\u89c1\u56fe3e\uff09<\/span>\u3002\u901a\u8fc7\u964d\u4f4e\u5c42\u95f4\u4f9d\u8d56\u7a0b\u5ea6\u53ef\u4ee5\u51cf\u8f7b\u8fd9\u79cd\u60c5\u51b5\uff0c\u5982\u679c\u964d\u4f4e\u5f97\u8db3\u591f\u591a\uff0c\u751a\u81f3\u53ef\u4ee5\u6062\u590d\u8fde\u7eed\u7684\u74e6\u89e3\u8fc7\u7a0b<\/span>\uff08\u89c1\u56fe3f\uff09<\/span>\u3002\u66f4\u91cd\u8981\u7684\u662f\uff0c\u5bf9\u516c\u5f0f\uff089\uff09\u81f3\uff0811\uff09\u7684\u5206\u6790\u63d0\u4f9b\u4e86\u5982\u4f55\u63d0\u9ad8\u76f8\u4e92\u4f9d\u8d56\u8026\u5408\u7cfb\u7edf\u9c81\u68d2\u6027\u7684\u89c1\u89e3\u3002\u76ee\u524d\u5df2\u8bc6\u522b\u51fa\u4e09\u79cd\u4e3b\u8981\u65b9\u6cd5\uff1a\u589e\u52a0\u81ea\u4e3b\u8282\u70b9\u7684\u6bd4\u4f8b\uff0c\u7279\u522b\u662f\u90a3\u4e9b\u9ad8\u5ea6\u6570\u7684\u8282\u70b9\uff1b\u5728\u76f8\u540c\u5ea6\u6570\u7684\u8282\u70b9\u4e4b\u95f4\u8bbe\u8ba1\u4f9d\u8d56\u5173\u7cfb\uff1b\u4ee5\u53ca\u7279\u522b\u6ce8\u91cd\u4fdd\u62a4\u9ad8\u5ea6\u503c\u8282\u70b9\u4e0d\u53d7\u6545\u969c\u548c\u653b\u51fb\u7684\u5f71\u54cd\u3002\u5728\u5927\u8111\u7f51\u7edc\u7684\u80cc\u666f\u4e0b\uff0c\u5982\u679c\u8003\u8651\u5230\u62d3\u6251\u76f8\u5173\u6027\uff0c\u53ef\u4ee5\u63d0\u9ad8\u7f51\u7edc\u5bf9\u76f8\u4e92\u4f9d\u5b58\u5f15\u53d1\u7684\u7ea7\u8054\u6548\u5e94\u7684\u9c81\u68d2\u6027\u3002\u6211\u4eec\u5efa\u8bae\u8bfb\u8005\u53c2\u8003\u6700\u8fd1\u7684\u7efc\u8ff0\u6587\u732e[162,163]\u53ca\u5176\u5f15\u7528\u6587\u732e\uff0c\u4ee5\u66f4\u6df1\u5165\u5730\u63a2\u8ba8\u8fd9\u7c7b\u7ea7\u8054\u7c7b\u578b\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u53e6\u4e00\u7c7b\u6a21\u578b\u8d77\u6e90\u4e8e\u96c6\u4f53\u884c\u4e3a\u7406\u8bba\uff0c\u5373\u6240\u8c13\u7684\u9608\u503c\u6a21\u578b<\/span>\uff08threshold model\uff09<\/span>\u3002\u5728\u8fd9\u4e9b\u6a21\u578b\u4e2d\uff0c\u6211\u4eec\u5047\u5b9a\u4e00\u4e2a\u8282\u70b9\u7684\u90bb\u5c45\u5bf9\u5176\u72b6\u6001\u6539\u53d8\u7684\u5f71\u54cd\u2014\u2014\u4e5f\u5c31\u662f\u4ece\u6b63\u5e38\u8fd0\u4f5c\u8f6c\u53d8\u4e3a\u5931\u6548\u2014\u2014\u5e76\u975e\u968f\u5931\u6548\u90bb\u5c45\u6570\u91cfn\u7ebf\u6027\u53d8\u5316\uff0c\u800c\u662f\u53ea\u5728\u8d85\u8fc7\u67d0\u4e2a\u9608\u503c\u540e\u624d\u4f1a\u8d77\u4f5c\u7528\u3002\u8fd9\u7c7b\u6a21\u578b\u901a\u5e38\u5e94\u7528\u4e8e\u793e\u4f1a\u5fc3\u7406\u5b66\u9886\u57df\uff0c\u4ee5\u4fbf\u7406\u89e3\u5728\u4ec0\u4e48\u6837\u7684\u60c5\u5883\u4e0b\uff0c\u793e\u4f1a\u884c\u52a8\u8005\u4f1a\u51b3\u5b9a\u4f20\u64ad\u8c23\u8a00\u3001\u6f6e\u6d41\u548c\u5047\u65b0\u95fb\uff0c\u6216\u91c7\u53d6\u7279\u5b9a\u884c\u4e3a\u3002\u8fd9\u4e2a\u95ee\u9898\u5f53\u7136\u4e0e\u793e\u4f1a\u5c42\u9762\u7684\u7f51\u7edc\u9c81\u68d2\u6027\u548c\u97e7\u6027\u5bc6\u5207\u76f8\u5173\uff1a\u4f17\u6240\u5468\u77e5\uff0c\u4fe1\u606f\u7684\u4f20\u64ad\u53ef\u80fd\u5bf9\u516c\u5171\u536b\u751f\u7cfb\u7edf\u6784\u6210\u4e25\u91cd\u5a01\u80c1\uff0c\u6781\u5316\u8fa9\u8bba\uff0c\u751a\u81f3\u7834\u574f\u516c\u4f17\u5bf9\u6c11\u4e3b\u5236\u5ea6\u7684\u4fe1\u4efb[167,168]\u3002\u4f46\u53e6\u4e00\u65b9\u9762\uff0c\u4fe1\u606f\u4f20\u64ad\u4e5f\u53ef\u80fd\u5e26\u6765\u79ef\u6781\u5f71\u54cd\uff0c\u4f8b\u5982\u4fc3\u8fdb\u521b\u65b0\u7b49[166,169]\u3002\u65e0\u8bba\u5982\u4f55\uff0c\u8fd9\u4e9b\u6a21\u578b\u90fd\u53ef\u4ee5\u8f7b\u677e\u5730\u5e94\u7528\u4e8e\u5176\u4ed6\u611f\u5174\u8da3\u9886\u57df\u4e2d\u53d1\u751f\u7684\u7ea7\u8054\u73b0\u8c61\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u9608\u503c\u6a21\u578b\u4e2d\uff0c\u90bb\u5c45\u5bf9\u8282\u70b9\u7684\u5f71\u54cd\u662f\u975e\u8fde\u7eed\u7684\u3001\u5206\u6bb5\u7684\uff0c\u8fd9\u79cd\u5f71\u54cd\u53ef\u4ee5\u901a\u8fc7\u591a\u79cd\u65b9\u5f0f\u5b9e\u73b0\u3002\u4e00\u79cd\u65b9\u6cd5\u662f\u5047\u8bbe\uff0c\u5982\u679c\u4e00\u4e2a\u8282\u70b9\u51fa\u73b0\u6545\u969c\u90bb\u5c45\u6bd4\u4f8b\u8d85\u8fc7\u67d0\u4e2a\u7279\u5b9a\u9608\u503c\uff0c\u90a3\u4e48\u8be5\u8282\u70b9\u5c06\u4f1a\u51fa\u73b0\u6545\u969c\u3002\u8fd9\u4e2a\u7b80\u5355\u6a21\u578b\u5bfc\u81f4\u4e86\u4e00\u7cfb\u5217\u4e30\u5bcc\u7684\u73b0\u8c61\uff0c\u7279\u522b\u662f\u5728\u53c2\u6570\u7a7a\u95f4\u4e2d\u754c\u5b9a\u7684\u4e24\u4e2a\u76f8\u53d8\uff0c\u4e00\u4e2a\u8fde\u7eed\u7684\u548c\u4e00\u4e2a\u975e\u8fde\u7eed\u7684<\/span>\uff08\u89c1\u56fe3g\u3001h\uff09<\/span>\u3002\u5b9e\u9645\u4e0a\uff0c\u5047\u5b9a\u521d\u59cb\u6545\u969c\u8282\u70b9\u6570\u91cf\u4e0e\u7cfb\u7edf\u89c4\u6a21\u76f8\u6bd4\u5c0f<\/span>\uff08\u53c2\u89c1\u6587\u732e[171,172]\u4e2d\u5173\u4e8e\u521d\u59cb\u7ea7\u8054\u64ad\u79cd\u7684\u4f5c\u7528\uff09<\/span>\uff0c\u5e76\u4e14\u6240\u6709\u8282\u70b9\u7684\u9608\u503c\u76f8\u540c<\/span>\uff08\u5f02\u8d28\u9608\u503c\u4e5f\u89c2\u5bdf\u5230\u7c7b\u4f3c\u73b0\u8c61[170]\uff09<\/span>\uff0c\u90a3\u4e48\u5f53\u9608\u503c\u8f83\u5927\u65f6\uff0c\u5168\u5c40\u7ea7\u8054\u975e\u5e38\u7f55\u89c1\u3002\u4f46\u662f\u5f53\u9608\u503c\u964d\u4f4e\u65f6\uff0c\u7f51\u7edc\u62d3\u6251\u5f00\u59cb\u53d1\u6325\u4f5c\u7528\u3002\u5982\u679c\u5e73\u5747\u5ea6\u503c\u592a\u5c0f\uff0c\u51e0\u4e4e\u6ca1\u6709\u8282\u70b9\u80fd\u591f\u4f20\u64ad\u6545\u969c\uff0c\u4e14\u8fd9\u4e9b\u8282\u70b9\u5f7c\u6b64\u5b64\u7acb\uff1b\u56e0\u6b64\uff0c\u5168\u5c40\u7ea7\u8054\u65e0\u6cd5\u5f62\u6210\u3002\u7136\u800c\uff0c\u5982\u679c\u5e73\u5747\u5ea6\u503c\u592a\u5927\uff0c\u56e0\u4e3a\u5927\u91cf\u6b63\u5e38\u8fd0\u4f5c\u7684\u90bb\u5c45\u4f1a\u7a33\u5b9a\u8282\u70b9\u4f7f\u5176\u59cb\u7ec8\u4f4e\u4e8e\u9608\u503c\uff0c\u7ea7\u8054\u65e0\u6cd5\u53d1\u5c55\u3002\u4e0b\u9650\u4e34\u754c\u5e73\u5747\u5ea6\u51e0\u4e4e\u4e0d\u4f9d\u8d56\u4e8e\u9608\u503c\uff0c\u800c\u4e0a\u9650\u4e34\u754c\u5e73\u5747\u5ea6\u5219\u5f3a\u70c8\u4f9d\u8d56\u4e8e\u5b83\u3002\u5728\u8fd9\u4e24\u4e2a\u70b9\u4e4b\u95f4\uff0c\u5bb9\u6613\u89e6\u53d1\u5168\u5c40\u7ea7\u8054\u3002\u5168\u5c40\u7ea7\u8054\u7684\u51fa\u73b0\u6761\u4ef6\u53ca\u5176\u89c4\u6a21\u4f30\u8ba1\u5df2\u6210\u529f\u63a8\u5e7f\u5230\u5177\u6709\u62d3\u6251\u5173\u8054\u6027\u7684\u7f51\u7edc\u3001\u65f6\u95f4\u548c\u591a\u5c42\u7f51\u7edc[173-180]\u3002\u7c7b\u4f3c\u5730\uff0c\u4eba\u4eec\u4e5f\u91c7\u7528\u4e86\u66f4\u590d\u6742\u7684\u6545\u969c\u6761\u4ef6\uff0c\u5982\u7ed3\u5408\u76f8\u5bf9\u548c\u7edd\u5bf9\u9608\u503c[181]\uff0c\u4ec5\u8bbe\u5b9a\u7edd\u5bf9\u9608\u503c[182]\uff0c\u6216\u5305\u62ec\u8fc7\u53bb\u6545\u969c\u66b4\u9732\u7684\u8bb0\u5fc6[183]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6211\u4eec\u5728\u8fd9\u90e8\u5206\u8ba8\u8bba\u7684\u6700\u540e\u4e00\u7ec4\u6a21\u578b\u662f\u8fc7\u8f7d\u6a21\u578b<\/span>\uff08overload model\uff09<\/span>\u3002\u5728\u8fd9\u4e9b\u6a21\u578b\u4e2d\uff0c\u8282\u70b9<\/span>\uff08\u6216\u8fde\u63a5\uff09<\/span>\u627f\u62c5\u7740\u4e00\u5b9a\u7684\u8d1f\u8f7d \u2014\u2014 \u4f8b\u5982\u7535\u7f51\u4e2d\u7684\u7535\u6d41\u3001\u4e92\u8054\u7f51\u4e2d\u7684\u6570\u636e\u5305\u3001\u516c\u5171\u4ea4\u901a\u7cfb\u7edf\u4e2d\u7684\u4e58\u5ba2\uff0c\u6216\u56fd\u9645\u8d38\u6613\u7f51\u7edc\u4e2d\u7684\u67d0\u79cd\u4ea7\u54c1<\/span>\uff08\u5982\u5c0f\u9ea6\u3001\u5927\u7c73\u548c\u7389\u7c73\uff09<\/span>\u3002\u8282\u70b9\u53ea\u8981\u5c06\u5176\u8d1f\u8377\u7ef4\u6301\u5728\u4e00\u4e2a\u9608\u503c\u4ee5\u4e0b\u2014\u2014\u4e5f\u5c31\u662f\u6240\u8c13\u7684\u5bb9\u91cf\u9650\u5236\u2014\u2014\u5c31\u80fd\u6b63\u5e38\u8fd0\u4f5c\uff0c\u800c\u8fd9\u4e2a\u5bb9\u91cf\u9650\u5236\u7406\u8bba\u4e0a\u53ef\u4ee5\u901a\u8fc7\u4eba\u4e3a\u5e72\u9884\u8fdb\u884c\u8c03\u6574\u3002\u5728\u53d1\u751f\u6545\u969c\u6216\u653b\u51fb\u4e4b\u540e\uff0c\u8d1f\u8377\u4f1a\u6839\u636e\u67d0\u4e9b\u89c4\u5219\u91cd\u65b0\u5206\u914d\uff0c\u8fd9\u4e9b\u89c4\u5219\u53d6\u51b3\u4e8e\u6240\u8981\u6a21\u62df\u7684\u7cfb\u7edf\u7c7b\u578b\uff0c\u53ef\u80fd\u5bfc\u81f4\u4e00\u7cfb\u5217\u8fc7\u8f7d\u548c\u65b0\u7684\u7f51\u7edc\u5185\u5206\u914d\u4e8b\u4ef6\u7684\u94fe\u5f0f\u53cd\u5e94\u3002\u7ea7\u8054\u5c06\u5728\u6240\u6709\u8282\u70b9\u7684\u8d1f\u8377\u6062\u590d\u81f3\u5176\u5bb9\u91cf\u4ee5\u4e0b\u65f6\u7ed3\u675f\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6c99\u5806\u6a21\u578b\u7684\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u662f\u6700\u5177\u4ee3\u8868\u6027\u7684\u8d1f\u8377\u91cd\u65b0\u5206\u914d\u673a\u5236\u4e4b\u4e00[184,185]\u3002\u8fd9\u4e9b\u6a21\u578b\u7684\u7279\u70b9\u662f\u7f13\u6162\u7684\u5916\u90e8\u9a71\u52a8<\/span>\uff08\u4f8b\u5982\uff0c\u901a\u8fc7\u5411\u7cfb\u7edf\u5f15\u5165\u8d1f\u8377\uff09<\/span>\u548c\u975e\u5e38\u5feb\u901f\u7684\u5f1b\u8c6b\u8fc7\u7a0b\uff0c\u5728\u6b64\u8fc7\u7a0b\u4e2d\u53d1\u751f\u7ea7\u8054<\/span>\uff08\u4f8b\u5982\uff0c\u901a\u8fc7\u8fc7\u8f7d\u8282\u70b9\u5411\u90bb\u5c45\u8f6c\u79fb\u8d1f\u8377\uff09<\/span>\u3002\u5f1b\u8c6b\u8fc7\u7a0b\u88ab\u8ba4\u4e3a\u6781\u5176\u8fc5\u901f\uff0c\u4ee5\u81f3\u4e8e\u5728\u5176\u6f14\u5316\u8fc7\u7a0b\u4e2d\u4e0d\u4f1a\u589e\u52a0\u4efb\u4f55\u8d1f\u8377\uff0c\u8fd9\u901a\u5e38\u5f88\u597d\u5730\u8fd1\u4f3c\u4e8e\u5b9e\u8bc1\u8fc7\u7a0b\uff0c\u56e0\u4e3a\u7ea7\u8054\u7684\u5c55\u5f00\u901a\u5e38\u662f\u6700\u5feb\u7684\u65f6\u95f4\u5c3a\u5ea6\u3002\u7531\u4e8e\u7f51\u7edc\u4e2d\u7684\u8282\u70b9\u5177\u6709\u4e0d\u540c\u6570\u91cf\u7684\u90bb\u5c45\uff0c\u5c06\u8282\u70b9\u5bb9\u91cf\u8bbe\u7f6e\u7b49\u4e8e\u5176\u5ea6\u503c\u6210\u4e3a\u4e00\u79cd\u81ea\u7136\u9009\u62e9[186]\uff0c\u5c3d\u7ba1\u8fd8\u6709\u5176\u4ed6\u9009\u62e9\u53ef\u80fd[187-189]\u3002\u6b64\u5916\uff0c\u4e3a\u4e86\u907f\u514d\u7f51\u7edc\u56e0\u8d1f\u8377\u8fc7\u8f7d\u800c\u9971\u548c\uff0c\u9700\u8981\u5728\u8f6c\u79fb\u8d1f\u8377\u65f6\u4ee5\u4e00\u5b9a\u7684\u6982\u7387\u79fb\u9664\u90e8\u5206\u8d1f\u8377\u3002\u5728\u76f8\u4e92\u4f9d\u8d56\u7684\u7535\u7f51\u80cc\u666f\u4e0b\u5df2\u7ecf\u5206\u6790\u8fc7\u51cf\u8d1f\u7ea7\u8054\u6a21\u578b\uff0c\u5728\u5176\u4e2d\u53d1\u73b0\u4e86\u4e00\u79cd\u4f18\u5316\u7f51\u7edc\u8026\u5408\u6c34\u5e73\u4ee5\u51cf\u5c11\u7ea7\u8054\u5f71\u54cd\u7684\u65b9\u6cd5[190]<\/span>\uff08\u89c1\u56fe3i\uff09<\/span>\u3002\u8fd8\u62a5\u544a\u4e86\u4e00\u4e9b\u6709\u8da3\u7684\u73b0\u8c61\u5b66\uff0c\u4f8b\u5982\u5f53\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u89c4\u5219\u4e0eKuramoto\u6a21\u578b\u76f8\u7ed3\u5408\u65f6\uff0c\u4f1a\u51fa\u73b0\u9f99\u738b\u4e8b\u4ef6<\/span>\uff08Dragon king events\uff09\uff08\u5373\u66f4\u5927\u7ea7\u8054\u4e2d\u7684\u7ea7\u8054\uff09<\/span>[191]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8fd8\u6709\u5176\u4ed6\u7684\u8d1f\u8377\u91cd\u65b0\u5206\u914d\u673a\u5236\u3002\u4e00\u79cd\u65b9\u6cd5\u662f\u901a\u8fc7\u6269\u5c55\u7ed3\u6784\u4e0e\u52a8\u529b\u5b66\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u5c06\u8d1f\u8377\u4e0e\u4ecb\u6570\u4e2d\u5fc3\u6027<\/span>\uff08betweenness\uff09<\/span>\u5173\u8054\u8d77\u6765\uff0c\u56e0\u4e3a\u6700\u77ed\u8def\u5f84\u4e0e\u4ea4\u901a\u6216\u8def\u7ebf\u5206\u914d\u4e4b\u95f4\u5b58\u5728\u6b63\u76f8\u5173\u6027[30]\u3002\u5728\u8be5\u6a21\u578b\u4e2d\uff0c\u6bcf\u4e2a\u8282\u70b9\u7684\u5bb9\u91cf\u4e0e\u5176\u521d\u59cb\u4ecb\u6570\u4e2d\u5fc3\u6027<\/span>\u6210\u6b63\u6bd4\uff0c\u5f53\u4e00\u4e2a\u8282\u70b9\u51fa\u73b0\u6545\u969c\u65f6\uff0c\u4f1a\u53d1\u751f\u5168\u5c40\u8d1f\u8377\u91cd\u65b0\u5206\u914d\uff0c\u53ef\u80fd\u5bfc\u81f4\u65b0\u7684\u8282\u70b9\u8fc7\u8f7d\uff0c\u8fd9\u4e9b\u8282\u70b9\u5e76\u4e0d\u4e00\u5b9a\u4f4d\u4e8e\u5148\u524d\u6545\u969c\u7684\u9644\u8fd1\u3002\u8fd9\u79cd\u975e\u5c40\u57df\u6027\u5728\u7a7a\u95f4\u5d4c\u5165\u7f51\u7edc\u4e2d\u5bb9\u6613\u88ab\u76f4\u89c2\u89c2\u5bdf\u5230[35]\u3002\u5bf9\u975e\u5c40\u57df\u6027\u8fdb\u884c\u5b8c\u6574\u3001\u660e\u786e\u7684\u8868\u5f81\u4ecd\u662f\u4e00\u9879\u5206\u6790\u6311\u6218\uff0c\u4f46\u5df2\u7ecf\u6709\u4e0d\u540c\u89c6\u89d2\u7684\u52aa\u529b\u65e8\u5728\u66f4\u597d\u5730\u7406\u89e3\u5176\u590d\u6742\u6027[192-195]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5177\u6709\u5f02\u6784\u7684\u5ea6\u5206\u5e03\u6216\u8005\u4ecb\u6570\u4e2d\u5fc3\u6027\u5206\u5e03\u7684\u7f51\u7edc\uff0c\u5982\u679c\u8282\u70b9\u5bb9\u91cf\u4e0d\u8db3\u591f\u5927\uff0c\u88ab\u53d1\u73b0\u5728\u9762\u5bf9\u9488\u5bf9\u6027\u653b\u51fb\u65f6\u6781\u5176\u8106\u5f31[196]\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5373\u4f7f\u53ea\u6709\u4e00\u4e2a\u8282\u70b9<\/span>\uff08\u9009\u62e9\u90a3\u4e9b\u4ecb\u6570\u4e2d\u5fc3\u6027\u6216\u5ea6\u6570\u6700\u5927\u7684\u8282\u70b9\u4e4b\u4e00\uff09<\/span>\u4f5c\u4e3a\u521d\u59cb\u538b\u529b\u6e90\u88ab\u7834\u574f\uff0c\u7f51\u7edc\u4e5f\u53ef\u80fd\u5d29\u6e83[30]\u3002\u76f8\u53cd\uff0c\u5373\u4f7f\u8282\u70b9\u7684\u5bb9\u91cf\u5f88\u4f4e\uff0c\u65e0\u8bba\u7f51\u7edc\u662f\u540c\u8d28\u8fd8\u662f\u5f02\u8d28\u8fde\u63a5\uff0c\u968f\u673a\u9009\u62e9\u4e00\u4e2a\u8282\u70b9\u4f5c\u4e3a\u521d\u59cb\u5e72\u6270\u5e76\u4e0d\u662f\u4e00\u79cd\u6709\u6548\u7684\u7b56\u7565\u6765\u7834\u574f\u7f51\u7edc\u3002\u7136\u800c\uff0c\u5df2\u7ecf\u5728\u5206\u6790\u4e0a\u8bc1\u660e\uff0c\u5bf9\u4e8e\u8db3\u591f\u5927\u7684\u968f\u673a\u9009\u62e9\u7684\u8282\u70b9\u96c6\u5408\uff0c\u7f51\u7edc\u53ef\u80fd\u906d\u53d7\u4e00\u4e2a\u4e0d\u8fde\u7eed\u7684\u74e6\u89e3\u76f8\u53d8[197]\u3002\u5728\u5355\u5c42\u548c\u591a\u5c42\u7f51\u7edc\u4e2d\u90fd\u6709\u62a5\u9053\u4e0d\u8fde\u7eed\u8f6c\u53d8\u7684\u6570\u503c\u8bc1\u636e[198]\u3002\u8fc7\u8f7d\u6a21\u578b\u8fd8\u5728\u94fe\u63a5\u6545\u969c\u548c\u5e72\u9884\u7684\u80cc\u666f\u4e0b\u8fdb\u884c\u4e86\u7814\u7a76[199-203]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u8ba8\u8bba\u4e86\u9759\u6001\u5e72\u9884\u7684\u62d3\u6251\u5f71\u54cd\u548c\u6709\u6548\u6027\uff0c\u4ee5\u53ca\u5c40\u90e8\u6545\u969c\u5982\u4f55\u5728\u5b8f\u89c2\u7f51\u7edc\u90e8\u5206\u4f20\u64ad\u7684\u4e0d\u540c\u673a\u5236\u3002\u5728\u4e0b\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4ecb\u7ecd\u4e92\u8865\u89c6\u89d2\uff0c\u5373\u5982\u4f55\u4ee5\u4e3b\u52a8\u548c\u9884\u8bbe\u7684\u65b9\u5f0f\u9632\u6b62\u548c\u5e94\u5bf9\u8fd9\u4e9b\u73b0\u8c61\u3002<\/span><\/section>\n

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    \n
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    <\/svg><\/section>\n<\/section>\n<\/section>\n
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    \u516d\u3001\u9632\u6b62\u548c\u5e94\u5bf9\u7f51\u7edc\u5d29\u6e83<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

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    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


    <\/p>\n

    \u7f51\u7edc\u5d29\u6e83\u53ef\u4ee5\u901a\u8fc7\u5728\u5176\u5f62\u6210\u9636\u6bb5\u5e94\u7528\u67d0\u4e9b\u8bbe\u8ba1\u539f\u5219\u6765\u9884\u9632\uff0c\u8fd9\u4e9b\u539f\u5219\u65e8\u5728\u63d0\u5347\u7f51\u7edc\u5bf9\u968f\u673a\u6545\u969c\u548c\u9488\u5bf9\u6027\u653b\u51fb\u7684\u97e7\u6027[204-208]\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u8bbe\u8ba1\u539f\u5219\u5e76\u975e\u603b\u662f\u5f97\u5230\u5e94\u7528\uff0c\u6216\u8005\u66f4\u7cdf\u7cd5\u7684\u662f\uff0c\u53ef\u80fd\u88ab\u5728\u7f51\u7edc\u6784\u5efa\u65f6\u65e0\u6cd5\u9884\u89c1\u7684\u9ad8\u7ea7\u653b\u51fb\u7b56\u7565\u6240\u89c4\u907f\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5373\u5c06\u53d1\u751f\u7684\u7f51\u7edc\u5d29\u6e83\u7684\u65e9\u671f\u9884\u8b66\u6307\u6807[68,209-214]\u4ee5\u53ca\u5bf9\u6b63\u5728\u53d1\u5c55\u7684\u5d29\u6e83\u8fdb\u884c\u7684\u4fee\u590d\u548c\u81ea\u9002\u5e94\u54cd\u5e94[215-217]\u6210\u4e3a\u6700\u4f73\u9632\u7ebf\u3002\u901a\u8fc7\u4fc3\u8fdb\u81ea\u53d1\u6062\u590d[218,219]\u6216\u901a\u8fc7\u5fae\u89c2\u5e72\u9884\u6765\u5f15\u53d1\u5d29\u6e83[215-217,220]\uff0c\u53ef\u80fd\u53ef\u4ee5\u9884\u9632\u7cfb\u7edf\u6027\u5d29\u6e83\u3002\u8fd9\u4e9b\u5e72\u9884\u5e94\u5f53\u91c7\u53d6\u6210\u672c\u6548\u76ca\u9ad8\u7684\u57fa\u4e8e\u7f51\u7edc\u7684\u7a0b\u5e8f[221,222]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7f51\u7edc\u8bbe\u8ba1\u7684\u65e9\u671f\u5c1d\u8bd5\u53ef\u4ee5\u8ffd\u6eaf\u52301970\u5e74\u4ee3\u7814\u7a76\u7684\u56fe\u589e\u5f3a\u95ee\u9898\u3002\u90a3\u65f6\u5f97\u51fa\u7684\u4e00\u4e2a\u6210\u679c\u662f\uff0c\u4f7f\u6709\u5411\u56fe\u5f3a\u8fde\u901a\u4ee5\u53ca\u65e0\u5411\u56fe\u8fde\u901a\u6216\u53cc\u8fde\u901a<\/span>\uff08\u5373\u79fb\u9664\u4efb\u4e00\u9876\u70b9\u540e\uff0c\u56fe\u4ecd\u4fdd\u6301\u8fde\u901a\u6027\uff09<\/span>\u6240\u9700\u7684\u6700\u5c11\u8fb9\u6570\u3002\u66f4\u8fd1\u671f\u7684\u7f51\u7edc\u8bbe\u8ba1\u7b56\u7565\u5219\u662f\u57282010\u5e74\u4ee3\u4e2d\u671f\u63d0\u51fa\u7684[204,205]\u3002\u7279\u522b\u662f\u5bf9\u4e8e\u65e0\u6807\u5ea6\u7f51\u7edc\u548c\u5177\u6709\u53cc\u5cf0\u5ea6\u5206\u5e03\u7684\u7f51\u7edc\uff0c\u5982\u679c\u9664\u4e86\u4e00\u4e2a\u8282\u70b9\u5916\uff0c\u6240\u6709\u8282\u70b9\u7684\u5ea6\u6570\u76f8\u540c\uff0c\u4e14\u63a5\u8fd1\u6bcf\u4e2a\u8282\u70b9\u7684\u5e73\u5747\u8fde\u63a5\u6570\uff0c\u540c\u65f6\u5269\u4e0b\u7684\u4e00\u4e2a\u8282\u70b9\u5177\u6709\u975e\u5e38\u5927\u7684\u5ea6\u6570k\u221dN2\/3<\/sup><\/span>\uff08\u5176\u4e2dN\u662f\u6784\u6210\u7f51\u7edc\u7684\u8282\u70b9\u6570\uff09<\/span>\uff0c\u90a3\u4e48\u53ef\u4ee5\u83b7\u5f97\u6700\u4f18\u7684\u9c81\u68d2\u6027[204]\u3002\u53e6\u4e00\u79cd\u65b9\u6cd5\u57fa\u4e8e\u7f51\u7edc\u6027\u80fd\u7684\u76f8\u5bf9\u4e0b\u964d\u53ca\u5176\u5728\u4e00\u7cfb\u5217\u6539\u8fdb<\/span>\uff08\u5305\u62ec\u589e\u52a0\u6216\u79fb\u9664\u7279\u5b9a\u94fe\u63a5\uff09<\/span>\u7684\u60c5\u51b5\u4e0b\u7684\u6700\u5c0f\u5316[205]\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u5982\u679cD\u8868\u793a\u53ef\u4ee5\u5bf9\u7f51\u7edcG\u9020\u6210\u7684\u4e00\u7ec4\u53ef\u80fd\u7684\u635f\u5bb3\uff0c<\/sub><\/span>\u662f\u4e00\u4e2a\u6620\u5c04\uff0c\u7ed9\u51fa\u4e86\u635f\u5bb3d\u2208<\/span>D\u4e4b\u540e\u7684\u65b0\u7f51\u7edc\uff0c\u5219\u635f\u5bb3d\u7684\u91cd\u8981\u6027\u7531\u6027\u80fd\u7684\u76f8\u5bf9\u4e0b\u964d<\/sub><\/span>\u7ed9\u51fa\uff0c\u5176\u4e2d<\/sub><\/span>\u3002\u6b64\u5916\uff0c\u5b9a\u4e49\u4e34\u754c\u635f\u5bb3d*\u2208D\u4e3a\u6700\u5c0f\u5316\u7684\u635f\u5bb3\u3002\u7136\u540e\u53ef\u4ee5\u5c06G\u56e0D\u800c\u4ea7\u751f\u7684\u8106\u5f31\u6027V\u5b9a\u4e49\u4e3a[205]\u3002<\/span><\/section>\n

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    <\/section>\n
    \u5176\u4e2d\uff0c <\/sub><\/span>\u662f\u7f51\u7edcG\u5728\u635f\u5bb3\u7c7b\u522bD\u4e0b\u7684\u6700\u5dee\u6027\u80fd\u3002\u540c\u6837\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6620\u5c04<\/sub><\/span>\u5b9a\u4e49\u4e00\u7ec4\u6539\u8fdbi\u2208I<\/span>\uff0c\u5bf9\u7f51\u7edcG\u8fdb\u884c\u6539\u8fdb\uff0c\u4ee5\u6b64\u5b9e\u73b0\u5728\u4e34\u754c\u6539\u8fdbi*\u6761\u4ef6\u4e0b\u7f51\u7edc\u7684\u6700\u4f18\u53ef\u63d0\u5347\u6027\u3002<\/span><\/section>\n

    <\/section>\n
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    <\/section>\n
    \u5176\u4e2d\uff0c<\/sub><\/span>\u662f\u5728\u6539\u8fdb\u7c7b\u522bI\u4e0b\uff0c\u7f51\u7edcG\u7684\u6700\u4f18\u6027\u80fd\u3002\u5173\u4e8e\u6539\u8fdbi\uff0c\u5176\u91cd\u8981\u6027\u7531\u6027\u80fd\u76f8\u5bf9\u589e\u52a0<\/sub><\/span>\u7ed9\u51fa\uff0c\u5176\u4e2d<\/sub><\/span>[205]\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u53ef\u4f18\u5316\u7684\u5185\u5bb9\u5b58\u5728\u4e00\u4e2a\u57fa\u672c\u9650\u5236\uff1a\u5b9e\u9645\u4e0a\uff0c\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u548c\u5176\u8868\u73b0\u662f\u96be\u4ee5\u540c\u65f6\u6700\u5927\u5316\u7684\u7ade\u4e89\u7279\u5f81[223]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7f51\u7edc\u8bbe\u8ba1\u7684\u6982\u5ff5\u5df2\u8fdb\u4e00\u6b65\u6269\u5c55\u81f3\u76f8\u4e92\u4f9d\u8d56\u7684\u7f51\u7edc\u4f53\u7cfb\u4e2d[206,162,224]\u3002\u4e00\u4e2a\u7f51\u7edc\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u4f9d\u8d56\u4e8e\u5176\u5185\u90e8\u7ed3\u6784\u4e0e\u4e0e\u5176\u4ed6\u7f51\u7edc\u8fde\u63a5\u6a21\u5f0f\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u4e3a\u4e86\u4f7f\u4e00\u4e2a\u4e92\u4f9d\u8d56\u7f51\u7edc\u5728\u8bbe\u8ba1\u4e0a\u88ab\u8ba4\u4e3a\u662f\u9c81\u68d2\u7684\uff0c\u5176\u76f8\u4e92\u8fde\u63a5\u5e94\u7531\u7f51\u7edc\u67a2\u7ebd\u8282\u70b9\u63d0\u4f9b\uff0c\u540c\u65f6\u7f51\u7edc\u95f4\u7684\u8fde\u63a5\u5e94\u9002\u5ea6\u96c6\u4e2d\u3002\u5982\u679c\u8fd9\u4e24\u4e2a\u6761\u4ef6\u5f97\u5230\u6ee1\u8db3\uff0c\u90a3\u4e48\u7f51\u7edc\u7cfb\u7edf\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u7a33\u5b9a\u7684\uff0c\u5e76\u4e14\u5bf9\u6545\u969c\u5177\u6709\u9c81\u68d2\u6027\u3002\u8fd9\u4e00\u7ed3\u679c\u4e5f\u5df2\u5728\u4efb\u52a1\u548c\u4f11\u606f\u72b6\u6001\u4e0b\u7684\u529f\u80fd\u6027\u5927\u8111\u7f51\u7edc\u5b9e\u9a8c\u4e2d\u5f97\u5230\u8bc1\u5b9e[206]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
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    <\/span><\/section>\n
    \u8fd1\u671f\u7684\u7814\u7a76\u8868\u660e\uff0c\u4e00\u53f0\u7ecf\u8fc7\u8bad\u7ec3\u7684\u673a\u5668\u80fd\u591f\u8bc6\u522b\u9ad8\u9636\u62d3\u6251\u6a21\u5f0f\uff0c\u4ece\u800c\u6709\u6548\u5730\u89e3\u6784\u5927\u89c4\u6a21\u7684\u793e\u4f1a\u3001\u57fa\u7840\u8bbe\u65bd\u548c\u6280\u672f\u7f51\u7edc[68]\uff0c\u5176\u6548\u7387\u751a\u81f3\u8d85\u8fc7\u4e86\u4eba\u7c7b\u7684\u542f\u53d1\u5f0f\u7b56\u7565\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u4e2a\u5e95\u5c42\u7a0b\u5e8f\u8fd8\u53ef\u4ee5\u8fdb\u884c\u53cd\u5411\u5de5\u7a0b \u2014\u2014 \u673a\u5668\u53ef\u4ee5\u8bc4\u4f30\u672a\u6765\u653b\u51fb\u5e26\u6765\u7cfb\u7edf\u89e3\u4f53\u7684\u6982\u7387 \u2014\u2014 \u4ece\u800c\u5f00\u53d1\u51fa\u7f51\u7edc\u5d29\u6e83\u7684\u9884\u8b66\u4fe1\u53f7\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u5982\u679cS0<\/sub>\u662f\u5bfc\u81f4\u7f51\u7edc\u6e17\u6d41\u7684\u865a\u62df\u79fb\u9664\u8282\u70b9\u96c6\uff0c\u4e14\u7b26\u5408\u4ee5\u4e0b\u7ea6\u675f<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n
    <\/span><\/section>\n

    <\/section>\n
    \u90a3\u4e48\uff0c\u5728\u79fb\u9664\u4e00\u7ec4\u901a\u7528\u8282\u70b9\u96c6S\u540e\uff0c\u7f51\u7edc\u7684\u9884\u8b66\u503c\u03a9\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u7ed9\u51fa\uff1a<\/span><\/section>\n

    <\/section>\n
    <\/section>\n

    <\/section>\n
    \u5176\u4e2d<\/sub><\/span>\uff0c\u8fd9\u91cc\u7684\u4e3b\u8981\u601d\u60f3\u662f\uff0c<\/sub><\/span>\u7528\u4e8e\u91cf\u5316\u7f51\u7edc\u5728\u5d29\u6e83\u524d\u80fd\u591f\u5bb9\u5fcd\u7684\u635f\u5bb3\u7a0b\u5ea6\u3002\u5f53\u7f51\u7edc\u7684\u5173\u952e\u8282\u70b9\u88ab\u79fb\u9664\u65f6\uff0c\u03a9 \u5feb\u901f\u63a5\u8fd1 1 [68]<\/span>\uff08\u89c1\u56fe 4\uff09<\/span>\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

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    <\/span><\/section>\n
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    <\/span><\/section>\n
    \u603b\u7684\u6765\u8bf4\uff0c\u672c\u8282\u8ba8\u8bba\u7684\u65b9\u6cd5\u63d0\u4f9b\u4e86\u9632\u6b62\u548c\u5e94\u5bf9\u7f51\u7edc\u5d29\u6e83\u6700\u5e38\u7528\u7684\u624b\u6bb5\uff0c\u540c\u65f6\uff0c\u5b83\u4eec\u4e5f\u5f88\u53ef\u80fd\u6210\u4e3a\u672a\u6765\u5728\u8fd9\u4e9b\u65b9\u5411\u53d1\u5c55\u7684\u6700\u80a5\u6c83\u7684\u571f\u58e4\u3002<\/span><\/section>\n


    <\/span><\/p>\n


    <\/section>\n

    \n
    \n
    \n
    \n
    \n

    <\/section>\n

    <\/section>\n
    \n
    <\/svg><\/section>\n<\/section>\n<\/section>\n
    \n

      \u4e03\u3001\u5c55\u671b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


    <\/p>\n

    \u6b63\u5982\u672c\u6587\u6240\u8ff0\uff0c\u7f51\u7edc\u74e6\u89e3\u76f8\u5173\u7684\u95ee\u9898\u4f17\u591a\uff0c\u5305\u62ec\u7406\u8bba\u6311\u6218\u4ee5\u53ca\u5f00\u53d1\u80fd\u5728\u5408\u7406\u65f6\u95f4\u5185\u74e6\u89e3\u5927\u578b\u7f51\u7edc\u7684\u7b97\u6cd5\u7684\u95ee\u9898\u3002\u5c3d\u7ba1\u81f3\u4eca\u6211\u4eec\u5df2\u7ecf\u53d6\u5f97\u4e86\u8bb8\u591a\u6210\u679c\uff0c\u4f46\u5728\u4e0a\u8ff0\u5404\u4e2a\u65b9\u9762\uff0c\u4ecd\u5b58\u5728\u6709\u5f85\u8fdb\u4e00\u6b65\u7814\u7a76\u7684\u5f00\u653e\u6027\u95ee\u9898\u3002<\/span><\/section>\n

    <\/span><\/section>\n
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    <\/span><\/section>\n
    \u4e3a\u5b9e\u73b0\u8fd9\u4e2a\u76ee\u7684\uff0c\u57fa\u4e8e\u590d\u6742\u7f51\u7edc\u6f5c\u5728\u51e0\u4f55\u7684\u74e6\u89e3\u65b9\u6cd5\u662f\u4e00\u4e2a\u6709\u6f5c\u529b\u7684\u7814\u7a76\u65b9\u5411[28]\u3002\u5c3d\u7ba1\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u65b9\u6cd5\u5df2\u5728\u6f5c\u5728\u7a7a\u95f4\u4e2d\u5f97\u5230\u5e94\u7528\uff0c\u4f46\u7f51\u7edc\u51e0\u4f55\u4e0e\u5176\u9c81\u68d2\u6027\u4e4b\u95f4\u7684\u8054\u7cfb\u8fd8\u672a\u6df1\u5165\u63a2\u8ba8\u3002\u8fd9\u4e00\u8ba4\u8bc6\u53ef\u80fd\u63a8\u52a8\u5f00\u53d1\u5168\u65b0\u7c7b\u578b\u7684\u7b97\u6cd5\uff0c\u7528\u4e8e\u7f51\u7edc\u7684\u7ed3\u6784\u548c\u529f\u80fd\u74e6\u89e3\uff0c\u540c\u65f6\u4e5f\u6709\u52a9\u4e8e\u63d0\u9ad8\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u548c\u97e7\u6027\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5c3d\u7ba1\u673a\u5668\u5b66\u4e60\u7b49\u4eba\u5de5\u667a\u80fd\u6280\u672f\u5df2\u5728\u8bf8\u5982\u81ea\u7136\u8bed\u8a00\u5904\u7406\u3001\u89c6\u9891\u548c\u56fe\u50cf\u5904\u7406\u7b49\u9886\u57df\u4ea7\u751f\u4e86\u91cd\u5927\u5f71\u54cd\uff0c\u4f46\u5728\u7f51\u7edc\u9886\u57df\u7684\u5f71\u54cd\u8fc4\u4eca\u76f8\u5bf9\u6709\u9650\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u5728\u6280\u672f\u3001\u7b97\u6cd5\u548c\u786c\u4ef6\u7406\u89e3\u65b9\u9762\u7684\u8fdb\u6b65\u65e0\u7591\u5c06\u5728\u4f17\u591a\u7f51\u7edc\u76f8\u5173\u4efb\u52a1\u4e2d\u53d1\u6325\u4f5c\u7528\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u603b\u4f53\u800c\u8a00\uff0c\u7406\u89e3\u7cfb\u7edf\u5982\u4f55\u5bf9\u5916\u90e8\u51b2\u51fb\u505a\u51fa\u53cd\u5e94\u548c\u9002\u5e94\u662f\u672a\u6765\u7684\u5173\u952e\u76ee\u6807\u3002\u9884\u8ba1\u7edf\u8ba1\u7269\u7406\u3001\u7f51\u7edc\u79d1\u5b66\u548c\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u4ea4\u53c9\u7814\u7a76\u5c06\u5728\u6b64\u76ee\u6807\u4e2d\u53d1\u6325\u57fa\u7840\u4f5c\u7528\u3002\u6f5c\u5728\u5e94\u7528\u8303\u56f4\u5e7f\u6cdb\uff0c\u4ece\u7ec6\u80de\u5c42\u9762\u2014\u2014\u9700\u8981\u9c81\u68d2\u6280\u672f\u6765\u8bc4\u4f30\u57fa\u56e0\u6216\u836f\u7269\u5e72\u9884\u7684\u6f5c\u5728\u5f71\u54cd\u2014\u2014\u5230\u6d41\u884c\u75c5\u5b66\u548c\u7ecf\u6d4e\u5b66\u9886\u57df\uff0c\u5728\u8fd9\u4e9b\u9886\u57df\uff0c\u51b2\u51fb\u53ef\u80fd\u6210\u4e3a\u7cfb\u7edf\u6027\u95ee\u9898\uff0c\u4ece\u800c\u5f71\u54cd\u793e\u4f1a\u7684\u7ed3\u6784\u548c\u529f\u80fd\u3002<\/span><\/section>\n

    <\/section>\n
    \u4ee3\u7801\uff1a\u7528\u4e8e\u6027\u80fd\u6bd4\u8f83\u7684\u4ee3\u7801\u53ef\u4ee5\u4ece\u4e0b\u8ff0\u76ee\u5f55\u4e2d\u627e\u5230<\/span><\/strong><\/section>\n
    https:\/\/github.com\/NetworkDismantling\/review.<\/span><\/section>\n


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    \u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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      <\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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      \uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n<\/section>\n<\/section>\n


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      \u9ad8\u9636\u7f51\u7edc\u793e\u533a<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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      \u968f\u7740\u5bf9\u73b0\u5b9e\u4e16\u754c\u63a2\u7d22\u7684\u4e0d\u65ad\u6df1\u5165\uff0c\u4eba\u4eec\u53d1\u73b0\u5728\u8bb8\u591a\u771f\u5b9e\u7684\u590d\u6742\u7cfb\u7edf\u4e2d\uff0c\u7ec4\u6210\u7cfb\u7edf\u7684\u4e2a\u4f53\u4e4b\u95f4\u4e0d\u4ec5\u5b58\u5728\u4e8c\u5143\u4ea4\u4e92\u5173\u7cfb\uff0c\u4e5f\u5e7f\u6cdb\u5b58\u5728\u591a\u4e2a\u4f53\u540c\u65f6\uff08\u6216\u4ee5\u7279\u5b9a\u987a\u5e8f\uff09\u8fdb\u884c\u4ea4\u4e92\uff0c\u5373\u9ad8\u9636\u4ea4\u4e92\u73b0\u8c61\u3002\u4e3a\u6b64\uff0c\u7814\u7a76\u4eba\u5458\u5206\u522b\u53d1\u5c55\u51fa\u4e86\u57fa\u4e8e\u8d85\u56fe\u3001\u5355\u7eaf\u590d\u5f62\u3001\u4f9d\u8d56\u5173\u7cfb\u7b49\u7684\u7f51\u7edc\u9ad8\u9636\u8868\u793a\u6a21\u578b\uff0c\u4e3a\u590d\u6742\u7f51\u7edc\u5206\u6790\u548c\u7814\u7a76\u63d0\u4f9b\u4e86\u65b0\u7684\u601d\u8def\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u7531\u7535\u5b50\u79d1\u6280\u5927\u5b66\u5415\u7433\u5a9b\u8001\u5e08\u3001\u4efb\u6653\u9f99\u8001\u5e08\u53ca\u4e2d\u56fd\u5730\u8d28\u5927\u5b66\uff08\u5317\u4eac\uff09\u7ba1\u9752\u8001\u5e08\u5728\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u53d1\u8d77\u4e86\u3010\u9ad8\u9636\u7f51\u7edc\u8bfb\u4e66\u4f1a<\/a><\/span>\u3011\u3002\u8bfb\u4e66\u4f1a\u56f4\u7ed5\u9ad8\u9636\u4ea4\u4e92\u7f51\u7edc\u7684\u57fa\u672c\u6982\u5ff5\u3001\u6a21\u578b\u3001\u65b9\u6cd5\u4e0e\u5e94\u7528\u7b49\u7814\u7a76\u8fdb\u884c\u7814\u8ba8\uff0c\u6309\u7167\u300c\u57fa\u7840\u7406\u8bba\u300d+\u300c\u6df1\u5165\u7406\u8bba\u300d+\u300c\u6848\u4f8b\u7814\u8ba8\u300d\u7684\u6a21\u5f0f\u5c55\u5f00\u3002\u8bfb\u4e66\u4f1a\u7b2c\u4e00\u5b63\u5df2\u7ecf\u5706\u6ee1\u7ed3\u675f\uff0c\u73b0\u5728\u62a5\u540d\u52a0\u5165\u53ef\u4ee5\u89e3\u9501\u7b2c\u4e00\u5b63\u5168\u90e8\u5f55\u64ad\u89c6\u9891\u5e76\u52a0\u5165\u793e\u7fa4\u4ea4\u6d41\u3002<\/span><\/section>\n


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      \u63a2\u7d22\u590d\u6742\u7cfb\u7edf\u9ad8\u9636\u4ea4\u4e92\u7684\u5965\u79d8 | \u9ad8\u9636\u7f51\u7edc\u8bfb\u4e66\u4f1a\u542f\u52a8<\/strong><\/a><\/p>\n<\/section>\n

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      \u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/p>\n

      1. <\/strong>Nature Physics\u8bc4\u8bba\uff1a\u590d\u6742\u7cfb\u7edf\u7684\u5185\u5728\u7b80\u5355\u6027<\/a><\/strong><\/span><\/section>\n
      2.<\/strong> Physics Reports\u91cd\u78c5\u7efc\u8ff0\uff1a\u7f51\u7edc\u97e7\u6027\u53ca\u6838\u5fc3\u7814\u7a76\u4e3b\u9898<\/a><\/strong><\/span><\/section>\n
      3. <\/strong><\/strong>\u5982\u4f55\u4ee5\u6700\u5c0f\u4ee3\u4ef7\u7834\u574f\u7cfb\u7edf\u7ed3\u6784\uff1f\u4e00\u5957\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u65b9\u6cd5<\/a><\/strong><\/strong><\/span><\/section>\n
      4. <\/strong><\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
      <\/a><\/strong><\/strong><\/span><\/section>\n
      5.<\/strong><\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
      6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


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      \u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/strong><\/section>\n

      <\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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