{"id":11823,"date":"2018-10-09T01:00:00","date_gmt":"2018-10-08T17:00:00","guid":{"rendered":"http:\/\/swarma.org\/%e8%a7%a3%e8%af%bb%e5%b9%82%e5%be%8b%e5%88%86%e5%b8%83%e4%b8%8e%e6%97%a0%e6%a0%87%e5%ba%a6%e7%bd%91%e7%bb%9c-%e9%95%bf%e6%96%87%e7%bb%bc%e8%bf%b0\/"},"modified":"2018-12-04T18:07:44","modified_gmt":"2018-12-04T10:07:44","slug":"%e8%a7%a3%e8%af%bb%e5%b9%82%e5%be%8b%e5%88%86%e5%b8%83%e4%b8%8e%e6%97%a0%e6%a0%87%e5%ba%a6%e7%bd%91%e7%bb%9c-%e9%95%bf%e6%96%87%e7%bb%bc%e8%bf%b0","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=11823","title":{"rendered":"\u89e3\u8bfb\u5e42\u5f8b\u5206\u5e03\u4e0e\u65e0\u6807\u5ea6\u7f51\u7edc | \u957f\u6587\u7efc\u8ff0"},"content":{"rendered":"
\n
\n

<\/strong><\/p>\n

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

\u660e\u65e5\u7ebf\u4e0a\u516c\u5f00\u8bfe\u9884\u544a<\/strong><\/strong><\/span><\/p>\n

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

\u60f3\u8981\u66f4\u597d\u5730\u4e86\u89e3\u5e42\u5f8b\u5206\u5e03\uff0c<\/span><\/p>\n

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10\u670810\u65e5 19:00-20:30 \u5e26\u4f60\u542f\u7a0b<\/span><\/span><\/strong><\/p>\n

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

\"\u96c6\u667a\"<\/p>\n

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

\u672c\u6587\u4ecb\u7ecd\u4e86\u5e42\u5f8b\u5206\u5e03\u7684\u5f62\u5f0f\u3001\u7279\u70b9\u4ee5\u53ca\u65e0\u6807\u5ea6\u7f51\u7edc\u7684\u5f62\u5f0f\u548c\u7279\u70b9<\/strong>\uff0c\u7279\u522b\u662f\u65e0\u6807\u5ea6\u7f51\u7edc\u5728\u4e8e\u62b5\u5fa1\u653b\u51fb\u548c\u4f20\u67d3\u75c5\u4f20\u64ad\u4e0a\u7684\u7279\u5f02\u6027\u3002\u5217\u4e3e\u4e86\u4e00\u4e9b\u7ecf\u5178\u7684\u5e42\u5f8b\u5206\u5e03\u968f\u673a\u53d8\u91cf\u751f\u6210\u673a\u5236\uff0c\u6700\u540e\u7b80\u4ecb\u4e86\u5bf9\u6570\u7ebf\u6027\u56de\u5f52\u548c\u6781\u5927\u4f3c\u7136\u5bf9\u4e8e\u5e42\u5f8b\u6307\u6570\u7684\u4f30\u8ba1\u65b9\u5f0f\u4ee5\u53caKS\u68c0\u9a8c\u5728\u5e42\u5f8b\u5206\u5e03\u68c0\u9a8c\u4e0a\u7684\u5e94\u7528\u3002<\/span><\/p>\n

\n

\u5c06\u56f4\u7ed5\u4ee5\u4e0b4\u4e2a\u95ee\u9898\u5c55\u5f00\uff1a<\/span><\/p>\n

    \n
  1. \n

    \u4ec0\u4e48\u662f\u5e42\u5f8b\u5206\u5e03<\/span><\/strong><\/p>\n<\/li>\n

  2. \n

    \u4ec0\u4e48\u662f\u65e0\u6807\u5ea6\u7f51\u7edc<\/span><\/strong><\/p>\n<\/li>\n

  3. \n

    \u5982\u4f55\u4ea7\u751f\u5e42\u5f8b\u5206\u5e03<\/span><\/strong><\/p>\n<\/li>\n

  4. \n

    \u5982\u4f55\u4f30\u8ba1\u548c\u5224\u65ad\u5e42\u5f8b\u5206\u5e03<\/span><\/strong><\/p>\n

    \n<\/li>\n<\/ol>\n

    \"\u96c6\u667a\"<\/p>\n

    \u5168\u6587\u6982\u5ff5\u5730\u56fe | \u672c<\/strong><\/span>\u6587\u7ea610000\u5b57\uff0c\u5efa\u8bae\u9605\u8bfb\u65f6\u95f430\u5206\u949f\u3002<\/span><\/strong><\/p>\n

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

    \n

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

    1.\u4ec0\u4e48\u662f\u5e42\u5f8b\u5206\u5e03<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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

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

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

    1.1 \u6b63\u6001\u5206\u5e03<\/strong><\/span><\/p>\n

    \uff08normal distribution\uff09<\/strong><\/span><\/p>\n

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

    \u76ee\u524d\uff0c\u5e42\u5f8b\u5206\u5e03\u8fd8\u6ca1\u6709\u8fdb\u5165\u6982\u7387\u8bba\u548c\u6570\u7406\u7edf\u8ba1\u7684\u6559\u6750\u3002\u4e3a\u4e86\u4fbf\u4e8e\u5927\u5bb6\u7406\u89e3\uff0c\u4ece\u5927\u5bb6\u719f\u77e5\u7684\u3001\u6559\u6750\u4e0a\u8bb2\u5f97\u6bd4\u8f83\u591a\u7684\u5206\u5e03\u5f00\u59cb\u8bf4\u8d77\u3002<\/span><\/p>\n

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

    1.1.1\u8eab\u9ad8\u5206\u5e03<\/span><\/strong><\/span><\/p>\n

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

    \u8bbe\u60f3\u4e00\u4e2a\u60c5\u51b5\uff0c\u5982\u679c\u8981\u4f30\u8ba1\u67d0\u4e2a\u4eba\u7684\u8eab\u9ad8\uff0c\u5982\u679c\u4f60\u5bf9\u8fd9\u79cd\u4eba\u79cd\u4e0d\u6e05\u695a\uff0c\u60f3\u5fc5\u4f60\u4e00\u5b9a\u96be\u4ee5\u56de\u7b54\u3002\u4f46\u5982\u679c\u7ed9\u4f60\u8db3\u591f\u591a\u7684\u8fd9\u79cd\u4eba\u4eba\u7ed9\u4f60\u89c2\u6d4b\uff0c\u4f60\u5c31\u4f1a\u6709\u4fe1\u5fc3\u8fdb\u884c\u9884\u6d4b\u3002\u4e3a\u4e86\u65b9\u4fbf\u9884\u6d4b\uff0c\u4f60\u4f1a\u5c06\u8fd9\u4e9b\u4eba\u6309\u8eab\u9ad8\u533a\u95f4\u8fdb\u884c\u7edf\u8ba1\uff0c\u7136\u540e\u505a\u51fa\u9891\u7387\u56fe\uff0c\u4e0d\u51fa\u610f\u5916\uff0c\u8fd9\u4e2a\u9891\u7387\u5e94\u8be5\u5982\u56fe1\u79cd\u7ea2\u8272\u6240\u793a\uff0c\u5448\u73b0\u51fa\u4e2d\u95f4\u9ad8\u4e24\u8fb9\u4f4e\u7684\u7279\u5f81\uff0c\u50cf\u4e00\u4e2a\u949f\u7684\u5f62\u72b6\u3002<\/span><\/p>\n

    \"\u96c6\u667a\"<\/p>\n

    \u56fe1 \u67d0\u4e00\u4e9b\u4eba\u53e3\u7684\u8eab\u9ad8\u5206\u5e03\u7279\u5f81\u56fe\u3002\u7ea2\u8272\u4e3a\u5b9e\u9645\u6837\u672c\uff0c\u7eff\u8272\u4e3a\u6b63\u6001\u5206\u5e03\u7684\u62df\u5408<\/span><\/span><\/strong><\/p>\n

    \u7ea2\u8272\u7684\u662f\u5b9e\u9645\u6570\u636e\uff0c\u800c\u7406\u8bba\u4e0a\u662f\u7eff\u8272\u56fe\u5f62\uff0c\u8fd9\u4e2a\u7406\u8bba\u5206\u5e03\u5c31\u662f\u8457\u540d\u7684\u6b63\u6001\u5206\u5e03\uff0c\u53c8\u540d\u9ad8\u65af\u5206\u5e03\uff08Gaussian distribution)<\/span>\uff0c\u53ef\u4ee5\u770b\u51fa\u8fd9\u548c\u5b9e\u9645\u7684\u5206\u5e03\u975e\u5e38\u4e00\u81f4\u3002<\/span><\/p>\n

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

    \u4ece\u8fd9\u4e2a\u4f30\u8ba1\u51fa\u7684\u671f\u671b\u548c\u6807\u51c6\u5dee\uff0c\u4f60\u5c31\u53ef\u4ee5\u56de\u7b54\u53ea\u8981\u662f\u8fd9\u79cd\u4eba\u79cd\u7684\u6210\u5e74\u7537\u6027\uff0c\u4ed6\u7684\u8eab\u9ad895%\u7684\u53ef\u80fd\u6027\u5e94\u8be5\u5728<\/span>\"\u96c6\u667a\"\u8fd9\u4e2a\u533a\u95f4\uff0c\u5176\u4e2d<\/span>\"\u96c6\u667a\"\u4e3a\u671f\u671b\uff0c<\/span>\"\u96c6\u667a\"\u4e3a\u6807\u51c6\u5dee\u3002<\/span><\/p>\n

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

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    1.1.2\u667a\u5546\u5206\u5e03<\/span><\/strong><\/p>\n

    \u8fd8\u53ef\u4ee5\u4e3e\u4e00\u4e2a\u4f8b\u5b50\uff0c\u5c31\u662f\u4eba\u7684\u667a\u5546\uff0c\u5982\u679c\u5927\u5bb6\u7528\u6709\u94b1\u53c8\u6709\u95f2\u7684\u8bdd\uff0c\u627e\u6765\u8db3\u591f\u591a\u7684\u4eba\u6d4b\u91cf\u4e00\u4e0b\u4ed6\u4eec\u7684\u667a\u5546\uff0c\u7136\u540e\u4e5f\u753b\u51fa\u667a\u5546\u7684\u5206\u5e03\uff0c\u4f60\u4e5f\u4f1a\u53d1\u73b0\u5b83\u4e5f\u662f\u670d\u4ece\u8fd9\u6837\u4e00\u4e2a\u4e2d\u95f4\u6bd4\u8f83\u9ad8\uff0c\u4e24\u8fb9\u8fc5\u901f\u8870\u51cf\u7684\u5206\u5e03\u56fe\uff08\u56fe2\uff09\u3002<\/span><\/p>\n

    \u4ece\u56fe\u4e0a\u53ef\u4ee5\u770b\u51fa\uff0c\u5927\u5bb6\u7684\u5e73\u5747\u667a\u5546\u5728\u4e00\u767e\uff0c\u53ea\u6709\u5f88\u5c11\u7684\u4eba\u80fd\u8dd1\u5f88\u8fdc\uff0c\u636e\u8bf4\u83ab\u624e\u7279\uff08Wolfgang Amadeus Mozart\uff09\uff0c\u7231\u56e0\u65af\u5766\uff08Alfred Einstein\uff09\u7684\u667a\u5546\u5f88\u9ad8\uff0c\u8fbe\u5230160\u4ee5\u4e0a\uff0c\u4f46\u53ea\u6709\u5343\u5206\u4e4b\u4e00\u7684\u4eba\u624d\u80fd\u6709\u8d44\u683c\u5982\u6b64\u9a84\u50b2\uff01\u8fdb\u4e00\u6b65\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba8\u8bba\u8fd9\u6837\u4e00\u4e2a\u95ee\u9898\u2014\u2014\u667a\u5546\u8fbe\u52301000\u7684\u4eba\u5b58\u5728\u5417\uff1f\u7b54\u6848\u662f\uff0c\u5982\u679c\u8fd9\u4e2a\u5206\u5e03\u662f\u5bf9\u7684\uff0c\u90a3\u4e48\u4eba\u7c7b\u4e0d\u53ef\u80fd\u8fbe\u5230\uff0c\u4e0d\u53ef\u80fd\u5728\u504f\u79bb\u671f\u671b\u90a3\u4e48\u8fdc\u7684\u5730\u65b9\u627e\u5230\u6b63\u6001\u5206\u5e03\u968f\u673a\u6570\u6837\u672c\u3002<\/span><\/p>\n

    \"\u96c6\u667a\"<\/p>\n

    \u56fe2 \u4eba\u7c7b\u667a\u5546\u5206\u5e03\u793a\u610f\u56fe<\/span><\/strong><\/p>\n

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    \"\u96c6\u667a\"\uff081\uff09<\/span><\/p>\n

    \u5176\u4e2d<\/span>\"\u96c6\u667a\"\u4e3a\u671f\u671b\uff0c<\/span>\"\u96c6\u667a\"\u4e3a\u6807\u51c6\u5dee\uff0c\u90fd\u662f\u6709\u9650\u7684\u6570\u503c\u3002<\/span><\/p>\n

    \u6b63\u6001\u5206\u5e03\u786e\u5b9e\u975e\u5e38\u5e7f\u6cdb\u5b58\u5728\uff0c\u5305\u62ec\u5b66\u751f\u7684\u6210\u7ee9\uff0c\u67d0\u4e00\u4eba\u79cd\u6210\u5e74\u7537\u4eba\u6216\u8005\u5973\u4eba\u7684\u4f53\u91cd\uff0c\u884c\u661f\u8f68\u9053\u7684\u504f\u5dee\uff0c\u4ee5\u53ca\u4e00\u4e9b\u5b9e\u9a8c\u4e0a\u7684\u8bef\u5dee\u7b49\u7b49\uff0c\u90fd\u662f\u5177\u6709\u8fd9\u79cd\u5206\u5e03\u7279\u5f81\u7684\u3002\u90a3\u4e48\u4e3a\u4ec0\u4e48\u8fd9\u79cd\u5206\u5e03\u666e\u904d\u5b58\u5728\uff1f<\/span><\/p>\n

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

    1.1.3\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406<\/span><\/strong><\/span><\/p>\n

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

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      \n
    • \n

      \u68e3\u83ab\u4f5b\uff0d\u62c9\u666e\u62c9\u65af\uff08de Moivre – Laplace\uff09\u5b9a\u7406<\/span><\/strong>\uff0c\u662f\u4e2d\u592e\u6781\u9650\u5b9a\u7406\u7684\u6700\u521d\u7248\u672c\uff0c\u8ba8\u8bba\u4e86\u670d\u4ece\u4e8c\u9879\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u3002\u5b83\u6307\u51fa\uff0cn \u4e2a\u53c2\u6570\u4e3a p\u7684\u4e8c\u9879\u5206\u5e03\u7684\u548c\u5c06\u4ee5np\u4e3a\u5747\u503c\u3001np(1-p)\u4e3a\u65b9\u5dee\u7684\u6b63\u6001\u5206\u5e03\u4e3a\u6781\u9650\u3002<\/span><\/p>\n<\/li>\n

    • \n

      \u6797\u5fb7\u4f2f\u683c\uff0d\u5217\u7ef4\uff08Lindeberg-Levy\uff09\u5b9a\u7406<\/span><\/strong>\uff0c\u662f\u68e3\u83ab\u4f5b\uff0d\u62c9\u666e\u62c9\u65af\u5b9a\u7406\u7684\u6269\u5c55\uff0c\u8ba8\u8bba\u72ec\u7acb\u540c\u5206\u5e03\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u7684\u4e2d\u592e\u6781\u9650\u5b9a\u7406\u3002\u5b83\u8868\u660e\uff0c\u72ec\u7acb\u540c\u5206\u5e03\u3001\u4e14\u6570\u5b66\u671f\u671b\u548c\u65b9\u5dee\u6709\u9650\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u7684\u6807\u51c6\u5316\u548c\u4ee5\u6807\u51c6\u6b63\u6001\u5206\u5e03\u4e3a\u6781\u9650\u3002<\/span><\/p>\n<\/li>\n

    • \n

      \u6797\u5fb7\u4f2f\u683c\uff0d\u8d39\u52d2\uff08Lindeberg-Feller\uff09\u5b9a\u7406<\/span><\/strong>\uff0c\u662f\u4e2d\u592e\u6781\u9650\u5b9a\u7406\u7684\u9ad8\u7ea7\u5f62\u5f0f\uff0c\u662f\u5bf9\u6797\u5fb7\u4f2f\u683c\uff0d\u5217\u7ef4\u5b9a\u7406\u7684\u6269\u5c55\uff0c\u8ba8\u8bba\u72ec\u7acb\uff0c\u4f46\u4e0d\u540c\u5206\u5e03\u7684\u60c5\u51b5\u4e0b\u7684\u968f\u673a\u53d8\u91cf\u548c\u3002\u5b83\u8868\u660e\uff0c\u6ee1\u8db3\u4e00\u5b9a\u6761\u4ef6\u65f6\uff0c\u72ec\u7acb\uff0c\u4f46\u4e0d\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u7684\u6807\u51c6\u5316\u548c\u4f9d\u7136\u4ee5\u6807\u51c6\u6b63\u6001\u5206\u5e03\u4e3a\u6781\u9650\u3002\u674e\u96c5\u666e\u8bfa\u592b\u4e5f\u7814\u7a76\u8ba8\u8bba\u4e86\u8fd9\u4e2a\u95ee\u9898\uff0c\u6709\u4e9b\u6750\u6599\u4e0a\u6807\u660e\u662f\u674e\u96c5\u666e\u8bfa\u592b\uff08Lyapunov\uff09\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n

      \u53ef\u4ee5\u7528\u9ad8\u5c14\u987f\uff08Francis Galton\uff09\u9489\u677f\u5b9e\u9a8c\u83b7\u5f97\u5bf9\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u7684\u7406\u89e3\u3002\u4e0b\u56fe\u662f\u4e00\u4e2a\u5b9e\u9a8c\u88c5\u7f6e\u3002\u6211\u4eec\u628a\u4e00\u4e9b\u94a2\u73e0\u653e\u5230\u4e0a\u9762\u7684\u5730\u65b9\uff0c\u7136\u540e\u5b83\u5c31\u4f1a\u4ece\u4e0a\u9762\u4e2d\u95f4\u7684\u8fd9\u4e2a\u5b54\u7684\u843d\u4e0b\u3002\u843d\u4e0b\u7684\u8fc7\u7a0b\u4e2d\uff0c\u5b83\u4f1a\u78b0\u5230\u4e00\u4e2a\u4e00\u4e2a\u7684\u9489\u5b50\uff0c\u78b0\u5230\u6bcf\u4e2a\u9489\u5b50\u7684\u65f6\u5019\uff0c\u5c0f\u7403\u90fd\u4f1a\u505a\u4e00\u4e2a\u9009\u62e9\uff0c\u8981\u4e48\u5f80\u5de6\u8fb9\u6eda\u4e0b\u53bb\uff0c\u8981\u4e48\u5f80\u53f3\u8fb9\u6eda\u4e0b\u53bb\u3002\u7ecf\u8fc7\u7b2c\u4e00\u5c42\u7684\u9009\u62e9\u540e\uff0c\u5c0f\u7403\u4f1a\u8fdb\u5165\u7b2c\u4e8c\u5c42\uff0c\u540c\u6837\u5b83\u4e5f\u4f1a\u9762\u4e34\u8fd9\u6837\u7684\u4e24\u4e2a\u9009\u62e9\uff0c\u5230\u5e95\u662f\u5f80\u5de6\u8fb9\u8d70\u5462\u8fd8\u662f\u5f80\u53f3\u8fb9\u8d70\uff1f<\/span><\/p>\n

      \u5047\u8bbe\u8fd9\u4e9b\u9489\u5b50\u7684\u8bbe\u8ba1\u6bd4\u8f83\u5747\u5300\u7684\uff0c\u5c0f\u7403\u6bcf\u4e00\u6b21\u8def\u5f84\u7684\u9009\u62e9\u90fd\u662f\u7b49\u6982\u7387\u4e8b\u4ef6\uff0c\u5411\u5de6\u8d70\u7684\u6982\u7387\u4e3a0.5\uff0c\u5411\u53f3\u8d70\u7684\u6982\u7387\u4e5f\u662f0.5\uff0c\u8fd9\u662f\u4e00\u4e2a\u7b49\u6982\u7387\u7684\u4e8c\u9879\u5206\u5e03\u3002\u5c0f\u7403\u7ecf\u8fc7\u4e00\u5c42\u662f\u4e00\u4e2a\u4e8c\u9879\u5206\u5e03\u7684\u9009\u62e9\uff0c\u662f\u4e00\u4e2a\u4e8c\u9879\u5206\u5e03\u7684\u968f\u673a\u6570\uff0c\u5176\u7ed3\u679c\u662f+1\u8fd8\u662f-1\uff0c\u800c\u4e00\u5c42\u4e00\u5c42\u7ecf\u8fc7\u5f88\u591a\u5c42\u540e\uff0c\u5b83\u5bf9\u4e8e\u4e2d\u5fc3\u4f4d\u7f6e\u7684\u504f\u5dee\u5b9e\u9645\u4e0a\u662f\u8fd9\u4e9b\u4e8c\u9879\u5206\u5e03\u968f\u673a\u6570\u7684\u548c\uff0c\u4ece\u5b9e\u9a8c\u7ed3\u679c\u4e0a\u770b\uff0c\u8fd9\u662f\u4e00\u4e2a\u6b63\u6001\u5206\u5e03\u3002<\/span><\/p>\n

      \u5927\u5bb6\u53ef\u4ee5\u60f3\uff0c\u5982\u679c\u6211\u4eec\u8981\u5c0f\u7403\u6eda\u5230\u56fe\u4e2d\u5230\u6700\u53f3\u8fb9\u7684\u5730\u65b9\uff0c\u5b83\u4e00\u5b9a\u8981\u662f\u7ecf\u8fc7\u591a\u6b21\u7684\u5f80\u53f3\u7684\u9009\u62e9\u624d\u4f1a\u5230\u8fbe\u8fd9\u4e2a\uff0c\u6bd4\u8f83\u56f0\u96be\u7684\uff0c\u6240\u4ee5\u6982\u7387\u6bd4\u8f83\u4f4e\u3002\u800c\u6700\u540e\u6eda\u5230\u4e2d\u95f4\u7684\u8def\u5f84\u9009\u62e9\u6bd4\u8f83\u591a\uff0c\u6982\u7387\u4e5f\u4f1a\u5927\u4e00\u4e9b\u3002<\/span><\/p>\n

      \u8fd9\u4e2a\u9489\u677f\u5b9e\u9a8c\u5b9e\u9645\u4e0a\u5c31\u662f\u8bf4\u660e\u68e3\u83ab\u4f5b\uff0d\u62c9\u666e\u62c9\u65af\u5b9a\u7406\u3002\u6269\u5c55\u5230\u5176\u4ed6\u5206\u5e03\uff0c\u540c\u5206\u5e03\u7684\u7d2f\u52a0\u6548\u679c\u53ef\u4ee5\u7531\u6797\u5fb7\u4f2f\u683c\uff0d\u5217\u7ef4\u5b9a\u7406\u6765\u786e\u5b9a\uff0c\u8fd9\u513f\u4e5f\u6709\u4e00\u4e9b\u8ba1\u7b97\u673a\u6a21\u62df\u7684\u56fe\u5f62[1]\uff0c\u8868\u660e\u4e00\u4e9b\u72ec\u7acb\u7684\u540c\u6837\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\uff0c\u5b83\u4eec\u548c\u6700\u540e\u90fd\u4f1a\u6210\u4e00\u4e2a\u6b63\u6001\u5206\u5e03\uff0c\u751a\u81f3\u5305\u62ecU\u578b\u7684\u5206\u5e03\uff0c\u4ece\u5355\u4e2a\u5206\u5e03\u6765\u770b\u4e2d\u95f4\u4f4e\u4e24\u8fb9\u9ad8\uff0c\u4f46\u591a\u4e2a\u72ec\u7acb\u7684\u8fd9\u79cd\u53d8\u91cf\u52a0\u8d77\u6765\uff0c\u6700\u540e\u4e5f\u4f1a\u5448\u73b0\u4e00\u4e2a\u6b63\u6001\u5206\u5e03\u3002 <\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe3 \u9ad8\u5c14\u987f\u9489\u677f\u5b9e\u9a8c\u88c5\u7f6e<\/span><\/p>\n

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

      1.2 \u5e42\u5f8b\u5206\u5e03<\/strong><\/span><\/p>\n

      \uff08power law distribution\uff09<\/span><\/strong><\/span><\/p>\n

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

      1.2.1\u5e42\u5f8b\u5206\u5e03\u7684\u51e0\u4e2a\u4f8b\u5b50<\/strong><\/span><\/p>\n

      \n

      \u6982\u7387\u8bba\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u544a\u8bc9\u6211\u4eec\uff0c\u5728\u590d\u6742\u7684\u591a\u56e0\u7d20\u60c5\u51b5\u4e0b\uff0c\u53ea\u8981\u4e2a\u4f53\u76f8\u4e92\u72ec\u7acb\uff0c\u96c6\u4f53\u6548\u679c\u5c31\u5e94\u8be5\u662f\u6b63\u6001\u5206\u5e03\u3002<\/strong>\u4f46\u4e16\u754c\u8fd9\u4e48\u5927\uff0c\u603b\u4f1a\u6709\u4f8b\u5916\u3002<\/strong><\/span><\/p>\n

      \n

      \u8fd9\u4e2a\u56fe\u662f\u5728\u7814\u7a76\u91d1\u878d\u5e02\u573a\u91cc\u9762\u53d1\u73b0\u7684\uff0c\u5c55\u73b0\u4e86\u6807\u51c6\u666e\u5c14500\u6307\u6570\u7684\u65e5\u6536\u76ca\u7387\u7684\u5206\u5e03\u3002\u5728\u91d1\u878d\u5e02\u573a\u91cc\u9762\uff0c\u80a1\u7968\u7684\u6536\u76ca\u7387\u65e0\u7591\u90fd\u662f\u5927\u5bb6\u5f88\u5173\u6ce8\u7684\uff0c\u6536\u76ca\u7387\u9ad8\u4ee3\u8868\u6323\u94b1\u591a\uff0c\u662f\u6295\u8d44\u8005\u6240\u5e0c\u671b\u7684\u3002<\/span><\/p>\n

      \n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe1.\u6807\u666e500\u6307\u6570\u7684\u6536\u76ca\u7387\u5206\u5e03\uff08\u7ea2\u7ebf\u4e3a\u6b63\u6001\u5206\u5e03\u7684\u62df\u5408\uff09<\/span><\/strong><\/span><\/p>\n

      \n

      \u8fd9\u4e2a\u5206\u5e03\u56fe\u4e5f\u5177\u6709\u4e2d\u95f4\u9ad8\u4e24\u8fb9\u4f4e\u7684\u7279\u5f81\uff0c\u548c\u6b63\u6001\u5206\u5e03\u6709\u70b9\u7c7b\u4f3c\u3002\u5b83\u5728\u6536\u76ca\u7387\u4e3a0\u7684\u9644\u8fd1\u662f\u4e00\u4e2a\u6bd4\u8f83\u9ad8\u7684\u5cf0\uff0c\u800c\u4e24\u8fb9\u662f\u5feb\u901f\u4e0b\u964d\u7684\uff0c\u8981\u6bd4\u6b63\u6001\u5206\u5e03\u4e0b\u964d\u5feb\u3002\u5982\u679c\u628a\u540c\u6837\u5747\u503c\u548c\u65b9\u5dee\u7684\u6b63\u6001\u5206\u5e03\u4e5f\u753b\u51fa\u6765\u7684\u8bdd\uff0c\u5dee\u5f02\u5c31\u4f1a\u66b4\u9732\u51fa\u6765\uff1a\u5b9e\u9645\u7684\u5206\u5e03\u5448\u73b0\u5c16\u5cf0\u80d6\u5c3e\u7684\u7279\u5f81\u3002<\/strong><\/span><\/p>\n

      \n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe2 \u7f8e\u56fd\u5bb6\u6237\u6536\u5165\u5206\u5e03\u548c\u5bcc\u8c6a\u7684\u8d44\u4ea7<\/span><\/strong><\/span><\/p>\n

      \n

      \u8fd9\u79cd\u4f8b\u5916\u5f88\u591a\uff0c\u6211\u4eec\u770b\u4e2a\u66f4\u6e05\u695a\u7684\u4f8b\u5b50\uff1a\u7f8e\u56fd\u7684\u5bb6\u6237\u6536\u5165\u6570\u636e\u3002\u53ef\u4ee5\u53d1\u73b0\u5b83\u597d\u50cf\u7c7b\u4f3c\u4e5f\u5c31\u8fd9\u79cd\u5c16\u5cf0\u80d6\u5c3e\u7684\u7279\u5f81\uff0c\u8981\u6bd4\u6b63\u6001\u5206\u5e03\u8868\u73b0\u5f97\u5cf0\u66f4\u52a0\u5c16\uff0c\u800c\u5c3e\u5df4\u4f1a\u62d6\u5f97\u66f4\u957f\u66f4\u539a\u3002<\/span><\/p>\n

      \n

      \u5047\u8bbe\u6536\u5165\u662f\u6b63\u6001\u5206\u5e03\uff0c\u6211\u4eec\u5c31\u4e0d\u80fd\u671f\u671b\u51fa\u73b0\u504f\u79bb\u671f\u671b\u8fbe\u523010\u500d\u6807\u51c6\u5dee\u90a3\u4e48\u5927\u7684\u6536\u5165\uff0c\u800c\u5b9e\u9645\u7684\u6536\u5165\u8ba9\u4eba\u5403\u60ca\uff0c\u4f60\u4f1a\u53d1\u73b0\u6709\u5f88\u591a\u4eba\uff0c\u4ed6\u4eec\u6709\u5de8\u989d\u7684\u6536\u5165\uff0c\u800c\u4e14\u6709\u5de8\u989d\u6536\u5165\u7684\u4eba\u4f1a\u6bd4\u4f60\u60f3\u8c61\u5f97\u591a\u3002<\/strong><\/span><\/p>\n

      \n

      \u56fe2(b)\u662f2015\u5e74\u798f\u5e03\u65af\u516c\u5e03\u7684\u7f8e\u56fd\u5bcc\u8c6a\u699c\uff0c\u8fd9\u91cc\u9762\u662f\u5217\u51fa\u7684\u4ed6\u4eec\u7684\u8d44\u4ea7\uff0c\u867d\u7136\u4e0d\u662f\u4e25\u683c\u5bf9\u5e94\u5230\u6536\u5165\u4e0a\uff0c\u4f46\u4e0d\u59a8\u788d\u6211\u4eec\u6765\u7406\u89e3\u8fd9\u4e2a\u4e8b\u60c5\u3002\u4ece\u6570\u636e\u4e0a\u770b\u51fa\u524d18\u4f4d\u5bcc\u8c6a\u4e2d\u7684\u6700\u540e\u4e00\u4e2a\u6709314\u4ebf\u7f8e\u5143\u7684\u5bb6\u4ea7\u3002\u8fd9\u662f\u4e00\u4e2a\u6570\u5b57\u662f\u4e00\u4e2a\u4ec0\u4e48\u6982\u5ff5\u5462\uff1f\u56fe2(c)\u662f2016\u5e74\u4e00\u4e9b\u56fd\u5bb6\u7684GDP\u6392\u540d\uff0c\u6392\u540d100\u7684\u62c9\u8131\u7ef4\u4e9a\u57282015\u5e74\u7684GDP\u662f312\u4ebf\u7f8e\u5143\u3002\u4e5f\u5c31\u610f\u5473\u7740\u670918\u4e2a\u5bcc\u8c6a\u7684\u8d22\u4ea7\u5927\u4e8e100\u591a\u4e2a\u56fd\u5bb6\u7684\u6574\u5e74\u7684GDP\u3002<\/strong><\/span><\/p>\n

      \n

      \u8fd9\u5c31\u662f\u4f20\u8bf4\u4e2d\u7684\u5bcc\u53ef\u654c\u56fd\u3002\u6211\u4eec\u4e0d\u77e5\u9053\u8fd9\u4e2a\u4e16\u754c\u4e0a\u8fd8\u6709\u8fd9\u4e48\u6709\u94b1\u7684\u4eba\uff0c\u800c\u66f4\u96be\u4ee5\u7f6e\u4fe1\u7684\u662f\u8fd9\u4e48\u6709\u94b1\u7684\u4eba\u8fd8\u90a3\u4e48\u7684\u591a\u3002<\/span><\/strong><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe3 \u5bcc\u4eba\u7684\u5bcc\u88d5\u7a0b\u5ea6\u4f1a\u8d85\u51fa\u6211\u4eec\u7684\u60f3\u8c61<\/span><\/strong><\/span><\/p>\n

      \u56fe\u7247\u6765\u6e90\uff1ahttps:\/\/www.huliwenku.com\/p\/ac9aqgdo.html<\/span><\/strong><\/span><\/p>\n

      \n

      1.2.2 \u5e42\u5f8b\u5206\u5e03\u7684\u6570\u5b66\u5f62\u5f0f\u548c\u56fe\u5f62\u8868\u8fbe<\/span><\/strong><\/span><\/p>\n

      \n

      \u5f62\u8c61\u7406\u89e3\u80d6\u5c3e\u7684\u542b\u4e49\uff0c\u5c31\u662f\u6709\u4e9b\u4e1c\u897f\u53ef\u4ee5\u8d85\u51fa\u60f3\u8c61\u7684\u5927\uff0c\u800c\u4e14\u51fa\u73b0\u8fd9\u4e48\u5927\u7684\u4e1c\u897f\u7684\u6982\u7387\u6bd4\u60f3\u8c61\u7684\u5927\uff08\u8fd9\u4e2a\u662f\u76f8\u5bf9\u6b63\u6001\u5206\u5e03\u6765\u8bb2\u7684\uff09\u3002<\/span><\/strong>\u8fd9\u79cd\u9661\u5ced\u800c\u5ef6\u4f38\u5f88\u957f\u7684\u5206\u5e03\u5c31\u662f\u6211\u4eec\u8981\u8bf4\u7684\u5e42\u5f8b\u5206\u5e03\uff0c\u5c31\u662f\u5206\u5e03\u51fd\u6570\u670d\u4ece\u5e42\u51fd\u6570<\/strong>\u3002\u5e42\u51fd\u6570\u7684\u6570\u5b66\u5f62\u5f0f\u4e3a<\/span><\/p>\n

      \"\u96c6\u667a\" \uff081\uff09<\/p>\n

      \u5bf9\u4e8e\u5e42\u5f8b\u5206\u5e03\u6709\u4e00\u4e2a\u66f4\u597d\u7684\u5c55\u793a\u65b9\u5f0f\uff0c\u5c31\u662f\u53cc\u5bf9\u6570\u5750\u6807<\/strong>\u3002\u5e42\u5f8b\u5206\u5e03\u51fd\u6570\u5462\u5728\u8fd9\u4e2a\u53cc\u5bf9\u6570\u5750\u6807\u4e0b\u5448\u73b0\u4e00\u4e2a\u975e\u5e38\u7b80\u6d01\u6f02\u4eae\u7684\u6027\u8d28\uff0c\u662f\u4e00\u4e2a\u8d1f\u659c\u7387\u7684\u76f4\u7ebf\u3002\u56fe7(b)\u5c31\u662f\u539f\u59cb\u7684\u76f4\u65b9\u56fe\u6211\u4eec\u6539\u6210\u4e86\u5bf9\u6570\u5750\u6807\u5f62\u6210\u7684\u3002\u56e0\u4e3a\u8fd9\u662f\u4e00\u4e2a\u6bd4\u8f83\u7eaf\u7684\u968f\u673a\u6570\u53d1\u751f\u5668\uff0c\u6240\u4ee5\u5b83\u4f1a\u751f\u6210\u5f97\u975e\u5e38\u597d\u3002<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe4 \u5e42\u5f8b\u5206\u5e03\u968f\u673a\u6570\u7684\u9891\u6570\u7edf\u8ba1\u76f4\u65b9\u56fe<\/span><\/strong>\uff08\u5728\u7ebf\u6027\u5750\u6807\u548c\u53cc\u5bf9\u6570\u5750\u6807\u4e0b\uff09<\/span><\/span><\/p>\n

      \u4e3a\u4ec0\u4e48\u4f1a\u51fa\u73b0\u4e00\u6761\u76f4\u7ebf\uff1f\u5176\u5b9e\u5f88\u7b80\u5355\uff0c\u5982\u679c\u6211\u4eec\u5bf9\u4e0a\u9762\u7684\u8fd9\u4e2a\u6982\u7387\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e24\u8fb9\u53d6\u5bf9\u6570\uff0c\u6211\u4eec\u5c31\u4f1a\u5f97\u5230\u8fd9\u6837\u4e00\u4e2a\u51fd\u6570\u5f62\u5f0f\u3002<\/span><\/p>\n

      \"\u96c6\u667a\" \uff082\uff09<\/p>\n

      \u8981\u6ce8\u610f\u5b9e\u9645\u4e0a\u7684\u6570\u5f80\u5f80\u4e0d\u4f1a\u6709\u8fd9\u4e48\u597d\u7684\u4e00\u81f4\u6027<\/strong>\u3002\u90a3\u5c31\u6709\u5fc5\u8981\u8ba8\u8bba\u4e00\u4e9b\u5b9e\u9645\u6570\u636e\u662f\u5426\u7b26\u5408\u5e42\u5f8b\uff0c\u5982\u4f55\u6765\u8fdb\u884c\u4f30\u8ba1\u548c\u63a8\u65ad\u8fd9\u4e2a\u95ee\u9898<\/strong>\u3002\u5b9e\u9645\u53ef\u80fd\u670d\u4ece\u5e42\u5f8b\u5206\u5e03\u7684\u6570\u636e\u8fd8\u6709\u90a3\u4e9b\u5462\uff1f\u6211\u4eec\u518d\u770b\u51e0\u4e2a\u4f8b\u5b50\u3002<\/span><\/p>\n

      \n

      1.2.3 \u5730\u9707\u7684\u80fd\u91cf<\/span><\/strong><\/p>\n

      \n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe5 \u5730\u9707\u7684\u80fd\u91cf\/\u9707\u7ea7\u548c\u53d1\u751f\u9891\u7387\u7684\u5173\u7cfb<\/span><\/strong><\/span><\/p>\n

      \u56fe\u50cf\u6765\u6e90\uff1a<\/span>Christensen, K., Danon, L., Scanlon, T., & Bak, P. (2002).Unified scaling law for earthquakes.Proceedings of the National Academy of Sciences<\/em>,99<\/em>(suppl 1), 2509-2513.<\/span><\/strong><\/span><\/p>\n

      \n

      \u56fe5\u662f\u5730\u9707\u7814\u7a76\u5f97\u5230\u7684\u4e00\u4e2a\u80fd\u91cf\u5206\u5e03\u56fe\u3002\u8fd9\u8868\u660e\u5730\u9707\u7684\u80fd\u91cf\u5206\u5e03\u5728\u53cc\u5bf9\u6570\u5750\u6807\u4e0b\u4e5f\u5927\u6982\u662f\u4e00\u6761\u76f4\u7ebf\uff01\u5927\u5bb6\u53ef\u80fd\u8ba4\u4e3a\u8fd9\u4e2a\u6a2a\u8f74\u662f\u9707\u7ea7\uff0c\u4e0d\u662f\u5bf9\u6570\u554a\u3002\u90a3\u662f\u56e0\u4e3a\u9707\u7ea7\u548c\u80fd\u91cf\u4e0d\u662f\u7ebf\u6027\u5173\u7cfb\uff0c\u9707\u7ea7\u76f8\u5dee1\uff0c\u80fd\u91cf\u5173\u7cfb\u4f1a\u670910\u500d\u7684\u5dee\u5f02\uff0c\u6240\u4ee5\u9707\u7ea7\u672c\u8eab\u662f\u5df2\u7ecf\u7c7b\u4f3c\u4e8e\u5bf9\u80fd\u91cf\u53d6\u4e86\u5bf9\u6570\u540e\u7684\u6307\u6807\u3002<\/strong>\u8fd9\u4e2a\u7eaf\u7cb9\u7684\u7269\u7406\u7cfb\u7edf\u8868\u73b0\u51fa\u5e42\u5f8b\u5206\u5e03\u7684\u884c\u4e3a\u7279\u5f81\u3002<\/span><\/p>\n

      \n

      1.2.4 \u57ce\u5e02\u89c4\u6a21<\/span><\/strong><\/span><\/p>\n

      \n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe6 \u57ce\u5e02\u89c4\u6a21\u7684\u5206\u5e03<\/span><\/strong><\/p>\n

      \u56fe\u50cf\u6765\u6e90\uff1a<\/span>Newman, M. E. (2005). Power laws, Pareto distributions and Zipf’s law.<\/span>Contemporary physics<\/em>,<\/span>46<\/em>(5), 323-351.<\/span><\/strong><\/p>\n

      \u590d\u6742\u7f51\u7edc\u7814\u7a76\u7684\u5927\u725bNewman\u57282005\u5e74\u53d1\u8868\u4e86\u4e00\u7bc7\u6587\u7ae0\uff0c\u5c55\u793a\u4e86\u57ce\u5e02\u89c4\u6a21\u7684\u5206\u5e03\uff0c\u5982\u56fe6\u6240\u793a\uff0c\u5de6\u56fe\u662f\u539f\u59cb\u7684\u5206\u5e03\uff0c\u53f3\u56fe\u662f\u53cc\u5bf9\u6570\u5750\u6807\uff0c\u53ef\u4ee5\u770b\u51fa\u660e\u663e\u7684\u76f4\u7ebf\u7279\u5f81\uff0c\u610f\u5473\u7740\u5e42\u5f8b\u5206\u5e03\u7279\u5f81\u3002\u57ce\u5e02\u7684\u751f\u6210\u548c\u7ef4\u6301\u662f\u4e00\u4e2a\u4eba\u7c7b\u548c\u81ea\u7136\u4ea4\u4e92\u5f62\u6210\u7684\u7ed3\u679c\uff0c\u8fd9\u4e2a\u7cfb\u7edf\u4e2d\u7684\u4e00\u4e9b\u73b0\u8c61\u4e5f\u80fd\u8868\u73b0\u51fa\u5e42\u5f8b\u5206\u5e03\u7279\u5f81\u3002<\/strong><\/span><\/p>\n

      \n

      1.2.5 \u56de\u4fe1\u7684\u65f6\u95f4\u95f4\u9694<\/strong><\/span><\/p>\n

      \n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe7 \u8fbe\u5c14\u6587\u548c\u7231\u56e0\u65af\u5766\u7684\u56de\u4fe1\u65f6\u95f4\u95f4\u9694\u5206\u5e03<\/span><\/strong><\/span><\/p>\n

      \u56fe\u50cf\u6765\u6e90\uff1a<\/span>Oliveira, J. G., & Barab\u00e1si, A. L.(2005). Human dynamics: Darwin and Einstein correspondence patterns.Nature<\/em>,437<\/em>(7063),1251.<\/span><\/strong><\/span><\/p>\n

      \u8fd9\u7bc7\u6587\u7ae0\u7814\u7a76\u7684\u5185\u5bb9\u5f88\u6709\u8da3\uff0c\u5b83\u8ba8\u8bba\u4e2a\u4eba\u7684\u56de\u4fe1\u65f6\u95f4\u7684\u957f\u5ea6\u5206\u5e03\uff0c\u4e00\u4e2a\u4eba\u6536\u5230\u4e00\u5c01\u4fe1\u518d\u56de\u4fe1\u7684\u65f6\u95f4\u5230\u5e95\u4f1a\u95f4\u9694\u591a\u5c11\u5929\uff1f<\/strong>\u770b\u8d77\u6765\u8fd9\u4e2a\u95ee\u9898\u5e94\u8be5\u662f\u4e0d\u597d\u56de\u7b54\u7684\uff0c\u8c01\u77e5\u9053\u4ed6\u6309\u4ec0\u4e48\u987a\u5e8f\u56de\u4fe1\u3002\u4f5c\u8005\u6536\u96c6\u5230\u7231\u56e0\u65af\u5766\uff08Albert Einstein\uff09\u548c\u8fbe\u5c14\u6587\uff08Charles Darwin\uff09\u8fd9\u4e24\u4e2a\u4eba\u7684\u53d1\u51fa\u7684\u90ae\u4ef6\u548c\u6536\u5230\u7684\u90ae\u4ef6\u505a\u4e86\u914d\u5bf9\uff0c\u7814\u7a76\u6587\u4ed6\u4eec\u6536\u5230\u4e00\u4e2a\u4fe1\u4e4b\u540e\uff0c\u591a\u5c11\u5929\u624d\u56de\u590d\u7684\u65f6\u95f4\u3002\u6700\u540e\u7684\u7ed3\u679c\u5982\u56fe7\u6240\u793a\uff0c\u5176\u4e2d(b)\u4e3a\u8fbe\u5c14\u6587\u7684\u56de\u4fe1\u60c5\u51b5\uff0c(c)\u4e3a\u7231\u56e0\u65af\u5766\u7684\u60c5\u51b5\u3002\u5927\u90e8\u5206\u4fe1\u5f88\u5feb\u5c31\u56de\u4e86\uff0c\u4f46\u662f\u6709\u5199\u4fe1\u5f88\u957f\u65f6\u95f4\u540e\u624d\u56de\u590d\u3002\u53ef\u4ee5\u53d1\u73b0\uff0c\u4ed6\u4eec\u5728\u53cc\u5bf9\u6570\u5750\u6807\u4e0b\u8868\u73b0\u4e3a\u76f4\u7ebf\uff0c\u8bf4\u660e\u5177\u6709\u5e42\u5f8b\u5206\u5e03\u7279\u5f81\uff0c\u751a\u81f3\u5e42\u5f8b\u6307\u6570\u51e0\u4e4e\u662f\u4e00\u6837\u7684\uff0c\u90fd\u57281.5\u3002<\/strong><\/span><\/p>\n

      \n

      \u5982\u679c\u56de\u4fe1\u7684\u65f6\u95f4\u662f\u5e42\u5f8b\u5206\u5e03\uff0c\u6211\u4eec\u5047\u8bbe\u7231\u56e0\u65af\u5766\u5df2\u7ecf\u6d3b\u4e861000\u5e74\uff0c\u4f60\u731c\u4ed6\u6700\u957f\u65f6\u95f4\u7684\u56de\u4fe1\u65f6\u95f4\u591a\u957f\uff1f\u8fd9\u5c06\u4f1a\u5f88\u96be\u4f30\u8ba1\uff0c\u56e0\u4e3a\u6709\u4e9b\u4fe1\u6839\u672c\u90fd\u6ca1\u6709\u60f3\u56de\u590d\u3002\u4f46\u5982\u679c\u5047\u8c61\u8fd9\u4e2a\u56de\u590d\u65f6\u95f4\u7684\u5206\u5e03\u662f\u6b63\u6001\u7684\uff0c\u90a3\u4e48\u53ea\u8981\u731c\u6d4b\u5728\u671f\u671b\u503c\u9644\u8fd1\u5c31\u597d\u4e86\u3002<\/span><\/p>\n

      \n

      1.2.6 \u5e42\u5f8b\u5206\u5e03\u7684\u671f\u671b\u548c\u65b9\u5dee<\/span><\/strong><\/span><\/p>\n

      \n

      \u6211\u4eec\u518d\u6765\u770b\u770b\u5e42\u5f8b\u5206\u5e03\u5728\u6570\u5b66\u4e0a\u662f\u5982\u4f55\u7a81\u7834\u6211\u4eec\u7684\u60f3\u50cf\u529b\u7684\u3002\u5bf9\u4e8e\u4efb\u4f55\u5206\u5e03\u6765\u8bb2\uff0c\u77e9\u662f\u5f88\u6709\u610f\u4e49\u7684\uff0c\u5b83\u4eec\u662f\u4e00\u4e2a\u4e2a\u6295\u5f71\uff0c\u80fd\u8868\u73b0\u8fd9\u4e2a\u5206\u5e03\u7684\u4e00\u4e9b\u7279\u5f81\u3002\u671f\u671b\u662f\u4e00\u9636\u539f\u70b9\u77e9\uff0c\u65b9\u5dee\u662f\u4e8c\u9636\u4e2d\u5fc3\u77e9\u3002\u5982\u679c\u77e5\u9053\u4e86\u8fd9\u4e24\u4e2a\u77e9\uff0c\u6574\u4e2a\u6b63\u6001\u5206\u5e03\u7684\u7279\u5f81\u5c31\u6e05\u695a\u4e86\u3002<\/strong><\/span><\/p>\n

      \n

      \u4f46\u662f\u7ecf\u8fc7\u6570\u5b66\u5206\u6790\uff0c\u4f60\u4f1a\u60ca\u8bb6\u5730\u53d1\u73b0\u5e42\u5f8b\u5206\u5e03\u968f\u673a\u6570\u7684\u65b9\u5dee\u603b\u662f\u4e0d\u5b58\u5728\u7684\uff0c\u5728\u4e00\u4e9b\u60c5\u51b5\u4e0b\uff0c\u8fde\u671f\u671b\u90fd\u4e0d\u5b58\u5728\u3002<\/strong><\/span><\/p>\n

      \n

      1.2.7 \u5e42\u5f8b\u5206\u5e03\u7684\u6807\u5ea6\u4e0d\u53d8\u6027<\/strong><\/span><\/p>\n

      \n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe8 \u5e42\u5f8b\u5206\u5e03\u7684\u6807\u5ea6\u4e0d\u53d8\u6027<\/span><\/strong><\/span><\/p>\n

      \u5e42\u5f8b\u5206\u5e03\u7684\u671f\u671b\u548c\u65b9\u5dee\u8ba9\u4eba\u610f\u5916\uff0c\u5b83\u8fd8\u6709\u4e00\u4e2a\u8ba9\u4eba\u610f\u5916\u7279\u5f81\uff0c\u88ab\u79f0\u4e3a\u6807\u5ea6\u4e0d\u53d8\u6027(scaling invariance)<\/strong>\u3002<\/span><\/p>\n

      \n

      \u5f62\u8c61\u5730\u8bf4\uff0c\u5c31\u50cf\u7528\u4e00\u4e2a\u653e\u5927\u955c\u89c2\u5bdf\u8fd9\u4e2a\u5206\u5e03\uff0c\u65e0\u8bba\u770b\u4ec0\u4e48\u7ec6\u8282\uff0c\u653e\u5927\u591a\u5c11\u500d\u6570\uff0c\u6240\u5f97\u5230\u7684\u6027\u8d28\u662f\u4e00\u6837\u7684\uff0c\u8fd9\u79cd\u73b0\u8c61\u88ab\u79f0\u4e3a\u65e0\u7279\u5f81\u5c3a\u5ea6<\/strong>\uff0c\u800c\u6b63\u6001\u5206\u5e03\u662f\u6709\u7684\uff0c\u5fc5\u987b\u6574\u4f53\u4e0a\u770b\u662f\u4e00\u4e2a\u949f\u7684\u5f62\u72b6\uff0c\u653e\u5927\u4efb\u4f55\u5c40\u90e8\u90fd\u4e0d\u4f1a\u5f97\u5230\u949f\u5f62\u7684\u56fe\u6848\u3002<\/span><\/p>\n

      \n

      \u8fd9\u8fd8\u53ef\u4ee5\u7528\u9a6c\u4e0a\u4f1a\u8bb2\u5230\u7684\u5e15\u7d2f\u625880\/20\u6cd5\u5219\u6765\u8bf4\uff0c80\/20\u6cd5\u5219\u8bf420%\u7684\u4eba\u53e3\u638c\u63e1\u4e8680%\u7684\u8d22\u5bcc\u3002\u800c\u5728\u8fd9\u4e2a\u638c\u63e1\u768480%\u8d22\u5bcc\u7684\u768420%\u4eba\u53e3\u4e2d\uff0c\u53c8\u670920%\u638c\u63e1\u4e86\u5176\u4e2d\u768480%\uff0c\u800c\u5728\u7a77\u4eba\u90e8\u5206\u968f\u4fbf\u5212\u51fa\u4e00\u90e8\u5206\uff0c\u4e5f\u4f1a\u53d1\u73b020%\u7684\u8f83\u4e3a\u5bcc\u6709\u7684\u5360\u6709\u4e86\u8fd9\u90e8\u5206\u7a77\u4eba\u603b\u8d22\u5bcc\u768480%\u3002\u5f53\u770b\u4efb\u4f55\u8d22\u5bcc\u7684\u533a\u95f4\uff0c\u90fd\u4f1a\u6709\u540c\u6837\u7684\u89c4\u5f8b\uff0c\u8fd9\u4e2a\u89c4\u5f8b\u548c\u6240\u5212\u5b9a\u7684\u533a\u95f4\u65e0\u5173\u3002<\/strong><\/span><\/p>\n

      \n

      1.2.8 \u9f50\u666e\u592b\u5f8b\uff08Zipf\u2019s law\uff09<\/strong><\/span><\/p>\n

      \n

      \u5728\u5e42\u5f8b\u5206\u5e03\u6982\u5ff5\u63d0\u51fa\u4ee5\u524d\uff0c\u5df2\u7ecf\u6709\u5f88\u591a\u4eba\u7814\u7a76\u7c7b\u4f3c\u7684\u73b0\u8c61\uff0c\u8fd9\u91cc\u9762\u8981\u4e24\u4e2a\u91cd\u8981\u4eba\u7269\uff0c\u4e00\u4e2a\u662f\u9f50\u666e\u592b\uff08G.K.Zipf\uff09<\/strong>\uff0c\u4e00\u4e2a\u662f\u5e15\u7d2f\u6258\uff08V. Pareto\uff09<\/strong>\u3002<\/span><\/p>\n

      \n

      Zipf\u63d0\u51fa\u4e86Zipf\u5f8b\uff0c\u5b9e\u9645\u4e0a\u5728\u4ed61932\u5e74\u548c1935\u5e74\u7814\u7a76\u4e0d\u540c\u8bed\u8a00\u7684\u8bcd\u9891<\/strong>\u7684\u65f6\u5019\u5c31\u8ba8\u8bba\u4e86\u8fd9\u4e2a\u89c4\u5f8b\uff0c\u628a\u67d0\u79cd\u8bed\u8a00\u7684\u6587\u672c\u6570\u636e\u62ff\u6765\uff0c\u5206\u5272\u6210\u8bcd\uff0c\u5206\u5b8c\u540e\u6570\u4e00\u4e0b\u4e0d\u540c\u7684\u8bcd\u5404\u51fa\u73b0\u4e86\u591a\u5c11\u6b21\uff0c\u7136\u540e\u4ece\u591a\u5230\u5c11\u6392\u5e8f\uff0c\u4f8b\u5982\u5bf9\u4e8e\u6c49\u8bed\u6765\u8bb2\u6392\u5728\u6700\u5de6\u8fb9\u7684\u662f\u201c\u7684\u201d\uff0c\u82f1\u8bed\u662f\u201cthe\u201d\u3002\u5c06\u7ed3\u679c\u753b\u5728\u56fe\u4e0a\uff0c\u6a2a\u8f74\u5c31\u662f\u6392\u5e8f\u5927\u5c0f\uff0c\u7eb5\u8f74\u5c31\u662f\u5bf9\u5e94\u7684\u8bcd\u51fa\u73b0\u7684\u6b21\u6570\uff0c\u5982\u56fe9\u6240\u793a\uff0c\u5728\u53cc\u5bf9\u6570\u5750\u6807\u4e0b\u5448\u73b0\u76f4\u7ebf\u7279\u5f81<\/strong>\u3002Zipf\u5f8b\u7684\u6570\u5b66\u8868\u8fbe\u662f<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe9 \u8bed\u8a00\u4e2d\u7684Zipf\u5f8b<\/span><\/strong><\/span><\/p>\n

      \"\u96c6\u667a\" \uff083\uff09<\/p>\n

      \n

      \u5176\u4e2d\uff0cx\u662f\u89c4\u6a21\uff0cr\u662f\u6392\u5e8f\uff0c\u03b2\u662fZipf\u6307\u6570\uff0c\u5728\u5f88\u591a\u60c5\u51b5\u4e0b\uff0c\u03b2=1\u3002\u6309\u73b0\u4ee3\u89c2\u70b9\u770b\uff0cZipf\u5f8b\u548cpower law\u5206\u5e03\u5b9e\u9645\u4e0a\u662f\u4e00\u81f4\u7684<\/strong>\uff0c\u8fd9\u4e2a\u5c06\u5728\u7a0d\u540e\u8ba8\u8bba\u3002<\/span><\/p>\n

      \n

      1.2.9 \u5e15\u7d2f\u6258\u6cd5\u5219\uff08Pareto principle\uff09\u548c\u5e15\u7d2f\u6258\u5206\u5e03\uff08Pareto distribution\uff09<\/strong><\/span><\/p>\n

      \n

      \u572819\u4e16\u7eaa90\u5e74\u4ee3\uff0cPareto\u6ce8\u610f\u5230\uff0c20%\u7684\u4eba\u53e3\u638c\u63e1\u610f\u5927\u5229\u7ea6\u670980%\u7684\u571f\u5730<\/strong>\u3002\u76ee\u524d\uff0c\u8fd9\u79cd\u201c80\/20\u201d\u539f\u5219\u5728\u7ba1\u7406\u9886\u57df\u6d41\u884c\u5ea6\u975e\u5e38\u9ad8\u3002<\/span><\/p>\n

      \n

      \u53ef\u4ee5\u5b9a\u4e49\u5e7f\u4e49\u7684Pareto\u6cd5\u5219\uff0cp<\/em>\u4efd\u989d\u7684\u4eba\u53e3\u5360\u636e\u603b\u8d22\u5bcc1-p<\/em>\u7684\u4efd\u989d\u3002\u5e76\u4e14\u8fd9\u4e2a\u89c4\u5f8b\u662f\u53ef\u4ee5\u8fed\u4ee3\u7684\uff0c\u5982p^2<\/em>\u4efd\u989d\u7684\u4eba\u53e3\u5360\u636e\u603b\u8d22\u5bcc\u7684\u4efd\u989d\uff0c\u4efd\u989d(1-p)^2<\/em>\u7684\u4eba\u53e3\u5360\u636e\u603b\u8d22\u5bcc\u7684\u4efd\u989d<\/strong>\uff0c\u5219\u53ef\u4ee5\u5f97\u5230Pareto\u5206\u5e03<\/span><\/p>\n

      \"\u96c6\u667a\" \uff084\uff09<\/p>\n

      \u8fd9\u662f\u4e00\u4e2a\u7d2f\u8ba1\u5206\u5e03\u51fd\u6570\uff0c\u8868\u793a\u5927\u4e8e\u67d0\u4e2a\u91cf\u7684\u4eba\u53e3\u4efd\u989d\u6b63\u6bd4\u4e8e\u8fd9\u4e2a\u91cf\u7684\u4e00\u4e2a\u5e42\u6b21\u51fd\u6570<\/strong>\uff0c\u4e3aPareto\u6307\u6570\uff0c\u5bf9\u4e8e\u5e7f\u4e49\u7684Pareto\u6cd5\u5219\uff0c\u5177\u6709\u5173\u7cfb[1]<\/span><\/p>\n

      \"\u96c6\u667a\"\uff085\uff09<\/p>\n

      Pareto\u6cd5\u5219\u548c\u5e15\u7d2f\u6258\u5206\u5e03\u662f\u7b49\u4ef7\u7684\u3002Pareto\u5206\u5e03\u5728\u53cc\u5bf9\u6570\u5750\u6807\u4e0b\u662f\u8d1f\u7684\u659c\u7387\u7684\u76f4\u7ebf\uff0c\u5982\u56fe10\u7684\u53f3\u56fe\u3002<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe10 \u5e42\u5f8b\u5206\u5e03\u548cPareto\u5206\u5e03<\/span><\/strong><\/p>\n

      \u6570\u636e\u6765\u6e90\uff1a<\/span>Newman, M. E. (2005). Power laws, Pareto distributions and Zipf’s law.Contemporary physics<\/em>,46<\/em>(5),323-351.<\/span><\/span><\/strong><\/p>\n

      \n

      1.2.10 Power Law\u5206\u5e03\u3001Zipf\u5f8b\u3001Pareto\u6cd5\u5219\u7684\u5173\u7cfb<\/span><\/strong><\/span><\/p>\n

      \n

      \u4ece\u56fe5\u3001\u56fe9\u548c\u56fe10\u53ef\u4ee5\u770b\u51fa\uff0c\u4e09\u8005\u90fd\u662f\u5728\u53cc\u5bf9\u6570\u5750\u6807\u5148\u8868\u73b0\u4e3a\u8d1f\u659c\u7387\u7684\u76f4\u7ebf<\/strong>\uff0c\u4f46\u4e09\u8005\u5750\u6807\u4e0d\u540c\uff0cZipf\u5f8b\u63cf\u8ff0\u4ece\u5927\u5230\u5c0f\u6392\u5e8f\u540e\u4f4d\u7f6er\u4e0e\u5904\u4e8e\u8be5\u5904\u7684\u5143\u7d20\u5c3a\u5ea6\u6216\u8005\u89c4\u6a21x\u4e4b\u95f4\u7684\u5173\u7cfb\uff08\u516c\u5f0f3\uff09\uff1bPareto\u5206\u5e03\u63cf\u8ff0\u7d2f\u8ba1\u5206\u5e03\u51fd\u6570\u7684\u6027\u8d28\uff0c\u5927\u4e8e\u7b49\u4e8e\u67d0\u4e00\u4e2a\u5c3a\u5ea6x\u7684\u603b\u6982\u7387\u6b63\u6bd4\u4e8ex\u7684\u4e00\u4e2a\u5e42\u51fd\u6570\uff08\u516c\u5f0f5\uff09\uff1b\u5e42\u5f8b\u5206\u5e03\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u7684\u6027\u8d28\uff0c\u8868\u660e\u67d0\u4e00\u4e2a\u5c3a\u5ea6x\u7684\u6982\u7387\u5bc6\u5ea6\u6b63\u6bd4\u4e8ex\u7684\u4e00\u4e2a\u5e42\u51fd\u6570\uff08\u516c\u5f0f1\uff09\u3002<\/span><\/p>\n

      \n

      \u4ee5\u73b0\u4ee3\u7684\u89c2\u70b9\u6765\u770b\uff0c\u8fd9\u4e09\u8005\u662f\u7b49\u4ef7\u7684\uff0c\u662f\u5bf9\u4e8e\u540c\u6837\u6570\u636e\u7684\u4e09\u79cd\u4e0d\u540c\u4fa7\u9762\u7684\u5c55\u793a\u3002<\/span><\/p>\n

      \n

      \u5148\u770b\u4e00\u4e2a\u7b80\u5355\u7684\u597d\u8bf4\u7684\uff0c\u5c31\u662fPareto\u5206\u5e03\u548c\u5e42\u5f8b\u5206\u5e03\u662f\u4e00\u56de\u4e8b\u3002\u4e3a\u4ec0\u4e48\uff1fPareto\u5206\u5e03\u8868\u73b0\u7684\u662f\u5c31\u662f\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u7684\u9006\u7d2f\u79ef\u5206\u5e03\u51fd\u6570<\/strong>\uff0c\u4ece\u67d0\u4e00\u4e2ax\u79ef\u5206\u5230\u65e0\u7a77\u5927\uff0c\u5e42\u5f8b\u51fd\u6570\u7684\u79ef\u5206\u8fd8\u662f\u5e42\u5f8b\u51fd\u6570\uff0c\u4f46\u5e42\u6307\u6570\u4f1a\u52a01\u3002\u6240\u4ee5\u5e42\u5f8b\u5206\u5e03\u5c31\u53ef\u4ee5\u901a\u8fc7\u9006\u7d2f\u79ef\u5206\u5e03\u5f97\u5230Pareto\u5206\u5e03\u3002\u76f8\u53cd\uff0c\u5982\u679c\u5bf9\u4e8ePareto\u5206\u5e03\u6c42\u5bfc\u6570\uff0c\u5c31\u53ef\u4ee5\u5f97\u5230\u5e42\u51fd\u6570\u5f62\u5f0f\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u3002\u6545\u4e8c\u8005\u662f\u7b49\u4ef7\u7684\u3002<\/span><\/p>\n

      \n

      \u5982\u679c\u5bf9\u4e8e\u9006\u7d2f\u79ef\u5206\u5e03\u4e58\u4e0a\u6837\u672c\u7684\u6570\u91cf\u5b9e\u9645\u4e0a\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a\u6392\u540d\uff0c\u5c31\u662f\u8fd9\u4e2a\u6392\u540d\u4e4b\u524d\u7684\u6837\u672c\u7684\u53d6\u503c\u5927\u4e8e\u5f53\u524d\u7684\u53d6\u503c\uff0c\u6216\u8005\u5f53\u524d\u7684x\u53d6\u503c\u7684\u6392\u540d\u5c31\u662f\u6837\u672c\u603b\u6570\u4e58\u4ee5Pareto\u5206\u5e03\u5728\u5f53\u524d\u6837\u672c\u7684\u53d6\u503c\u3002Pareto\u5206\u5e03\u548cZipf\u5f8b\u5b9e\u9645\u4e0a\u662f\u98a0\u5012\u4e86\u6a2a\u8f74\u548c\u7eb5\u8f74\uff0c\u4ed6\u4eec\u4ece\u56fe\u5f62\u4e0a\u662f\u5173\u4e8ey=x\u5bf9\u79f0\u7684<\/strong>\u3002\u5bf9\u6570\u76f4\u7ebf\u7684Pareto\u5206\u5e03\u7b49\u4ef7\u4e8e\u5bf9\u4e8e\u76f4\u7ebf\u7684Zipf\u5f8b\uff0c\u659c\u7387\u4e92\u4e3a\u5012\u6570\u3002\u7efc\u4e0a\uff0c\u8fd9\u4e09\u8005\u662f\u540c\u4e00\u4e2a\u6570\u636e\u7684\u4e0d\u540c\u5c55\u793a\u5f62\u5f0f\uff0c\u5728\u53cc\u5bf9\u6570\u5750\u6807\u4e0b\u5747\u4e3a\u8d1f\u659c\u7387\u7684\u76f4\u7ebf\uff0c\u4e14\u6ee1\u8db3\u5173\u7cfb<\/strong><\/span><\/p>\n

      \"\u96c6\u667a\" \uff086\uff09<\/p>\n

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

      \n

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

      2.\u590d\u6742\u7f51\u7edc<\/span><\/strong><\/p>\n

      \u4e0e\u65e0\u6807\u5ea6\u7f51\u7edc<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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

      2.1 \u590d\u6742\u7f51\u7edc<\/strong><\/span><\/p>\n

      (complex network)\u548c\u5ea6(degree)<\/span><\/strong><\/span><\/p>\n

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

      \u4e16\u754c\u5f88\u590d\u6742\uff0c\u7279\u522b\u662f\u4eba\u7684\u53c2\u4e0e\u4f1a\u589e\u52a0\u5176\u4e0d\u786e\u5b9a\u6027\u548c\u66f4\u4e3a\u590d\u6742\u7684\u5173\u7cfb\u3002\u590d\u6742\u7684\u7cfb\u7edf\u4f1a\u5448\u73b0\u8bf8\u591a\u5c5e\u6027\u548c\u7279\u5f81\uff0c\u5404\u4e2a\u5c5e\u6027\u4e4b\u95f4\u7684\u5173\u8054\u9519\u7efc\u590d\u6742\uff0c\u4ece\u590d\u6742\u7684\u7cfb\u7edf\u6293\u4f4f\u6700\u6838\u5fc3\u7684\u56e0\u7d20\u548c\u4f5c\u7528\u673a\u5236\u662f\u80fd\u6210\u529f\u5206\u6790\u7cfb\u7edf\u5e94\u7528\u7cfb\u7edf\u7684\u5fc5\u7531\u4e4b\u8def\u3002<\/span><\/h2>\n

      <\/h2>\n

      \u590d\u6742\u7f51\u7edc\u662f\u4eba\u7c7b\u8ba4\u8bc6\u590d\u6742\u4e16\u754c\u7684\u4e00\u4e2a\u5178\u578b\u5de5\u5177\u3002<\/span><\/h2>\n

      <\/h2>\n

      \u5728\u7814\u7a76\u4e00\u4e9b\u5177\u4f53\u7684\u4f8b\u5b50\u65f6\uff0c\u53ef\u4ee5\u505a\u4e00\u4e9b\u7b80\u5316\uff0c\u590d\u6742\u7f51\u7edc\u5c31\u662f\u5bf9\u4e8e\u771f\u5b9e\u7cfb\u7edf\u7b80\u5316\u5f97\u6765\u7684\u3002\u4f8b\u5982\u7814\u7a76\u6d88\u606f\u5728\u793e\u4f1a\u4e2d\u7684\u4f20\u64ad\uff0c\u5047\u5982\u4e2a\u4f53\u4e0d\u638c\u63e1\u8bf8\u5982CCTV\u8fd9\u6837\u7684\u5a92\u4f53\u4fe1\u606f\uff0c\u90a3\u4e48\u5f88\u591a\u6d88\u606f\u662f\u901a\u8fc7\u793e\u4f1a\u5173\u7cfb\uff08\u7279\u522b\u662f\u670b\u53cb\u5173\u7cfb\uff09\u4f20\u9012\u51fa\u53bb\u7684\uff0c\u6240\u4ee5\u670b\u53cb\u5173\u7cfb\u5c31\u662f\u6d88\u606f\u4f20\u64ad\u7684\u91cd\u8981\u8f7d\u4f53\u3002\u5728\u7814\u7a76\u6d88\u606f\u4f20\u64ad\u65f6\uff0c\u6211\u4eec\u4e0d\u7528\u8003\u8651\u4ed6\u4eec\u7a7f\u4ec0\u4e48\u8863\u670d\uff0c\u4e5f\u53ef\u4ee5\u7b80\u5316\u6027\u522b\u5dee\u5f02\u7684\u5f71\u54cd\uff0c\u6700\u540e\u53d1\u73b0\u6700\u6838\u5fc3\u7684\u5f71\u54cd\u4f20\u64ad\u884c\u4e3a\u7684\u5c31\u662f\u8fd9\u4e2a\u793e\u4f1a\u5173\u7cfb\u7f51\uff0c\u5728\u8fd9\u4e2a\u7f51\u7edc\u4e2d\u4e2a\u4f53\u88ab\u62bd\u8c61\u4e3a\u8282\u70b9\uff0c\u5173\u7cfb\u88ab\u62bd\u8c61\u4e3a\u8fde\u8fb9\uff0c\u4e2a\u4f53\u7684\u751f\u7269\u529f\u80fd\u7b49\u5b8c\u5168\u4e0d\u7528\u8003\u8651\uff0c\u8282\u70b9\u7684\u552f\u4e00\u529f\u80fd\u5c31\u662f\u901a\u8fc7\u8fde\u8fb9\u4f20\u9012\u4fe1\u606f\u3002<\/span><\/h2>\n

      <\/h2>\n

      \u56fe11\u662f\u4e00\u4e2a\u793e\u4f1a\u5173\u7cfb\u7f51\u7edc\u7684\u793a\u610f\u56fe\uff0c\u5de6\u8fb9\u8868\u793a\u4e00\u4e2a\u975e\u5e38\u5c40\u90e8\u7684\u7f51\u7edc\uff0c\u4e2a\u4eba\u4e3a\u8282\u70b9\u800c\u5177\u6709\u670b\u53cb\u5173\u7cfb\u5c31\u4f1a\u5728\u76f8\u5e94\u7684\u8282\u70b9\u4e4b\u95f4\u8fde\u4e00\u6761\u8fb9\u3002\u8282\u70b9\u7684\u8fde\u8fb9\u6570\u91cf\u79f0\u4e3a\u5ea6(degree)\uff0c\u56fe11\uff08b\uff09\u4e2d\u7684\u4e24\u4e2a\u4eba\uff08\u5728\u5176\u4ed6\u7684\u4eba\u90fd\u53ea\u67092-3\u4e2a\u5ea6\u7684\u65f6\u5019\uff09\u7684\u5ea6\u662f5\uff0c\u5728\u8fd9\u4e2a\u5c40\u90e8\u533a\u57df\u7684\u4fe1\u606f\u4f20\u9012\u4e2d\u4e00\u5b9a\u4f1a\u8d77\u5230\u91cd\u8981\u7684\u4f5c\u7528\u3002<\/span><\/h2>\n

      <\/h2>\n

      \u6574\u4e2a\u793e\u4f1a\u5173\u7cfb\u7f51\u53ef\u80fd\u5982\u56fe11\uff08b\uff09\u4e00\u6837\uff0c\u5f88\u591a\u7684\u8282\u70b9\u7684\u5ea6\u4f1a\u5f88\u5c0f\uff0c\u800c\u4e00\u4e9b\u8282\u70b9\u7684\u5ea6\u5f88\u5927\uff0c\u5fae\u535a\u4e0a\u4e00\u4e9b\u5927V\u7684\u7c89\u4e1d\u60ca\u4eba\u5730\u591a\uff0c\u4ed6\u4eec\u5728\u6d88\u606f\u7684\u4f20\u9012\u4e0a\u5177\u6709\u76f8\u5f53\u9ad8\u7684\u8bdd\u8bed\u6743\u3002\u8fd9\u79cd\u5ea6\u7684\u5206\u5e03\uff08\u5747\u8861\u7a0b\u5ea6\uff09\u5bf9\u4e8e\u7f51\u7edc\u7684\u529f\u80fd\u5177\u6709\u91cd\u8981\u5f71\u54cd\u3002<\/span><\/h2>\n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe11<\/span><\/strong><\/span>\u793e\u4f1a\u5173\u7cfb\u7f51<\/span><\/strong><\/p>\n

      \u56fe\u50cf\u6765\u6e90\uff1a<\/span><\/strong>https:\/\/business-networksw.org\/page\/30\/?pages-list<\/span><\/strong><\/span><\/p>\n

      \n
      \n
      <\/p>\n

      2.2 \u65e0\u6807\u5ea6\u7f51\u7edc<\/strong><\/span><\/p>\n

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

      2.2.1 \u65e0\u6807\u5ea6\u7f51\u7edc\u7684\u5b9a\u4e49<\/strong><\/span><\/p>\n

      \n

      \u65e0\u6807\u5ea6\u7f51\u7edc\uff08scalefree network\uff09\u662f\u590d\u6742\u7f51\u7edc\u5927\u725bA.-L. Barabasi\u57281999\u5e74\u63d0\u51fa\u7684\u6982\u5ff5\uff0c\u7b80\u5355\u5730\u8bf4\u5c31\u662f\u5ea6\u5206\u5e03\u670d\u4ece\u5e42\u5f8b\u5206\u5e03\u7684\u7f51\u7edc<\/span><\/strong>\u3002\u4ed6\u57282018\u5e74\u91cd\u65b0\u8bb2\u8ff0\u4e86\u4ed6\u5982\u6b64\u547d\u540d\u7684\u539f\u56e0\u2014\u2014\u201cWe named these networks scale-free, inspired by the scale-free nature of power laws observed in the vicinity of phase transitions.\u201d[2]\u3002\u65e0\u6807\u5ea6\u7f51\u7edc\u4e2d\u5176\u5404\u8282\u70b9\u4e4b\u95f4\u7684\u8fde\u63a5\u72b6\u51b5\uff08\u5ea6\u6570\uff09\u5177\u6709\u4e25\u91cd\u7684\u4e0d\u5747\u5300\u5206\u5e03\u6027\uff1a\u7f51\u7edc\u4e2d\u5c11\u6570\u79f0\u4e4b\u4e3aHub\u70b9\u7684\u8282\u70b9\u62e5\u6709\u6781\u5176\u591a\u7684\u8fde\u63a5\uff0c\u800c\u5927\u591a\u6570\u8282\u70b9\u53ea\u6709\u5f88\u5c11\u91cf\u7684\u8fde\u63a5\u3002\u5c11\u6570Hub\u70b9\u5bf9\u65e0\u6807\u5ea6\u7f51\u7edc\u7684\u8fd0\u884c\u8d77\u7740\u4e3b\u5bfc\u7684\u4f5c\u7528\u3002<\/strong><\/span><\/p>\n

      \n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe12\u4e00\u4e9b\u5b9e\u9645\u7f51\u7edc\u4e2d\u7684\u5ea6\u5206\u5e03\u53ef\u4ee5\u8fd1\u4f3c\u7531\u5e42\u5f8b\u5206\u5e03\u8868\u793a<\/span><\/strong><\/span><\/p>\n

      \u56fe\u50cf\u6765\u6e90\uff1a<\/span>Barab\u00e1si, A. L., & Albert, R. (1999). Emergence ofscaling in random networks.science<\/em>,286<\/em>(5439),509-512.<\/span><\/span><\/strong><\/span><\/p>\n

      Barabasi\u7684\u8fd9\u7bc7\u6587\u7ae0\u662f\u65e0\u6807\u5ea6\u7f51\u7edc\u7814\u7a76\u91cc\u9762\u975e\u5e38\u8457\u540d\u7684\u4e00\u7bc7\uff0c\u81f3\u4eca\u5df2\u7ecf\u5f15\u7528\u4e863\u4e07\u591a\u6b21\u3002\u5728\u8fd9\u7bc7\u6587\u7ae0\u91cc\u9762\u67093\u4e2a\u4f8b\u5b50\uff0c\u7b2c\u4e00\u4e2a\u6700\u5de6\u8fb9\u7684\u662f\u6f14\u5458\u5408\u4f5c\u7f51<\/strong>\uff0c\u7b2c\u4e8c\u4e2a\u662f\u4e07\u7ef4\u7f51<\/strong>\uff0c\u7b2c\u4e09\u4e2a\u662f\u4e00\u4e2a\u7535\u529b\u7f51<\/strong>\u3002<\/span><\/p>\n

      \n

      \u5728\u6f14\u5458\u5408\u4f5c\u7f51\u7edc\u4e2d\uff0c\u6f14\u5458\u662f\u8282\u70b9\uff08\u7fa4\u4f17\u6f14\u5458\u4e0d\u7b97\uff09\uff0c\u5982\u679c\u4e24\u4e2a\u4eba\u51fa\u6f14\u8fc7\u4e00\u90e8\u5f71\u7247\uff0c\u5c31\u662f\u6709\u4e00\u6b21\u5408\u4f5c\uff0c\u5c31\u8fde\u4e0a\u8fb9\u3002\u7ecf\u5e38\u51fa\u6f14\u7684\u660e\u661f\u5c31\u4f1a\u6709\u673a\u4f1a\u548c\u5f88\u591a\u4e0d\u540c\u7684\u4eba\u5408\u4f5c\uff0c\u4f8b\u5982\u5468\u661f\u9a70\u3001\u6210\u9f99\u5c31\u6bd4\u8f83\u591a\uff0c\u800c\u5176\u4ed6\u4eba\u7684\u5ea6\u5c31\u4f1a\u5c11\u4e00\u4e9b\u3002\u800c\u8fd9\u4e9b\u8282\u70b9\u7684\u5ea6\u4f5c\u4e3a\u968f\u673a\u6570\u5177\u6709\u5e42\u5f8b\u5206\u5e03\u7279\u5f81\uff0c\u6709\u4e9b\u4eba\u7684\u5ea6\u4f1a\u5927\u5f97\u8d85\u51fa\u5f88\u591a\u4eba\u7684\u60f3\u8c61<\/strong>\u3002\u8865\u5145\u4e00\u4e2a\u4f8b\u5b50\uff0c\u6570\u5b66\u5bb6P. Erd\u0151s\u4e00\u751f\u4e2d\u540c500\u591a\u4f4d\u5408\u4f5c\u8005\u53d1\u8868\u8d85\u8fc71450\u7bc7\u6570\u5b66\u8bba\u6587\uff0c\u65e0\u8bba\u4ece\u5408\u4f5c\u8005\u7684\u6570\u91cf\u8fd8\u662f\u53d1\u8868\u6587\u7ae0\u7684\u7bc7\u6570\u90fd\u8ba9\u4eba\u60ca\u53f9\u3002<\/span><\/p>\n

      \n

      \u4e07\u7ef4\u7f51\u662f\u5404\u4e2a\u7f51\u7ad9\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u4ed6\u4eec\u901a\u8fc7\u9875\u9762\u94fe\u63a5\u5efa\u7acb\u5173\u7cfb\uff0c\u8fd9\u79cd\u5ea6\u5206\u5e03\u7684\u5e42\u5f8b\u7279\u5f81\u8bf4\u660e\u7edd\u5927\u90e8\u5206\u7f51\u7ad9\u6ca1\u6709\u591a\u5c11\u4e0e\u7ad9\u5916\u7684\u4e92\u94fe\uff0c\u4f46\u6709\u4e00\u4e9b\u7f51\u7ad9\u6709\u5f88\u591a\u4e0e\u5176\u4ed6\u7f51\u7ad9\u7684\u94fe\u63a5<\/strong>\uff0c\u4f8b\u5982\u4e00\u4e9b\u95e8\u6237\u7f51\u7ad9\uff0c\u5982\u4e2d\u56fd\u7684\u65b0\u6d6a\u7f51\u3002<\/span><\/p>\n

      \n

      \u5982\u679c\u7ed9\u5b9a\u7f51\u7edc\u8282\u70b9\uff0c\u4efb\u610f\u8282\u70b9\u4e4b\u95f4\u4ee5\u76f8\u540c\u7684\u6982\u7387\u8fde\u4e00\u6761\u8fb9\u5c31\u6784\u6210\u968f\u673a\u7f51\u7edc\uff08ER network\uff09\u3002\u8fd9\u4e2a\u7f51\u7edc\u7ecf\u5e38\u88ab\u7528\u6765\u548c\u5176\u4ed6\u7f51\u7edc\u8fdb\u884c\u7ed3\u6784\u548c\u529f\u80fd\u4e0a\u7684\u5bf9\u6bd4\u7814\u7a76\u3002\u5982\u56fe13\uff08a\uff09\u8fd9\u4e2a\u7f51\u7edc\u4e2d\u5ea6\u5206\u5e03\u5177\u6709\u6bd4\u8f83\u96c6\u4e2d\u7684\u8303\u56f4\uff0c\u4e0d\u4f1a\u5b58\u5728\u5ea6\u5f88\u5927\u7684\u8282\u70b9\uff0c\u5c3e\u90e8\u5448\u73b0\u6307\u6570\u4e0b\u964d\u7279\u5f81\uff0c\u4e0e13\uff08b\uff09\u7f51\u7edc\u7ed3\u6784\u5177\u6709\u5f88\u5927\u5dee\u5f02\u3002\u66f4\u6709\u610f\u601d\u7684\u662f\uff0c\u65e0\u6807\u5ea6\u7f51\u7edc\u5177\u6709\u4e00\u4e9b\u4ee4\u4eba\u60ca\u8bb6\u7684\u529f\u80fd\u7279\u5f81\u3002<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe13 \u4e00\u4e9b\u5b9e\u9645\u7f51\u7edc\u4e2d\u7684\u5ea6\u5206\u5e03\u53ef\u4ee5\u8fd1\u4f3c\u7531\u5e42\u5f8b\u5206\u5e03\u8868\u793a<\/span><\/strong><\/span><\/p>\n

      \u56fe\u7247\u6765\u6e90\uff1a<\/span>Albert, R., Jeong, H.,& Barab\u00e1si, A. L. (2000). Error and attack tolerance of complex networks.nature<\/em>,406<\/em>(6794), 378.<\/strong><\/span><\/p>\n

      \n

      2.2.2 \u65e0\u6807\u5ea6\u7f51\u7edc\u7684\u9c81\u68d2\u4e14\u8106\u5f31\u6027<\/span><\/strong><\/span><\/p>\n

      \n

      \u65e0\u6807\u5ea6\u7f51\u7edc\u7684\u9c81\u68d2\u4e14\u8106\u5f31\u6027\u4f3c\u4e4e\u663e\u5f97\u6709\u77db\u76fe\uff0c\u9c81\u68d2\u6027\u8bf4\u660e\u80fd\u591f\u62b5\u6297\u5e72\u6270\uff0c\u8106\u5f31\u6027\u8bf4\u660e\u4e0d\u80fd\u62b5\u5fa1\u5e72\u6270\u3002<\/span><\/strong>\u8fd9\u4e24\u4e2a\u77db\u76fe\u7684\u4e1c\u897f\u600e\u4e48\u80fd\u591f\u96c6\u6210\u5728\u4e00\u4e2a\u7f51\u7edc\u4e2d\u5462\uff1f2000\u5e74\u7684\u65f6\u5019\uff0cBarabasi\u7b49\u4eba\u5199\u4e86\u4e00\u7bc7\u6587\u7ae0\uff0c\u7528\u968f\u673a\u7f51\u7edc\u548c\u65e0\u6807\u5ea6\u7f51\u7edc\u8fdb\u884c\u5bf9\u6bd4\u7814\u7a76\uff0c\u8ba8\u8bba\u4e86\u8282\u70b9\u968f\u673a\u5931\u6548\u548c\u88ab\u6709\u610f\u56fe\u653b\u51fb\u7684\u4e0d\u540c\u7ed3\u679c\u3002<\/span><\/p>\n

      \n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe14\u65e0\u6807\u5ea6\u7f51\u7edc\u5bf9\u4e8e\u968f\u673a\u5931\u6548\u7684\u9c81\u68d2\u6027\u548c\u5bf9\u4e8e\u6709\u76ee\u7684\u653b\u51fb\u7684\u8106\u5f31\u6027<\/span><\/strong><\/span><\/p>\n

      \u56fe\u7247\u6765\u6e90\uff1aAlbert, R., Jeong, H.,& Barab\u00e1si, A. L. (2000). Error and attack tolerance of complex networks.nature,406(6794), 378.<\/span><\/strong><\/span><\/p>\n

      \n

      \u5982\u56fe14\u6240\u793a\uff0c\u6a2a\u8f74\u4e3a\u79fb\u9664\u7684\u8282\u70b9\u6bd4\u4f8b\uff0c\u968f\u673a\u5931\u6548\u60c5\u51b5\u4e0b\u968f\u673a\u79fb\u9664\u8282\u70b9\uff0c\u6709\u610f\u653b\u51fb\u65f6\u5019\u4ece\u5ea6\u6700\u5927\u7684\u8282\u70b9\u5f00\u59cb\u79fb\u9664\u3002\u7eb5\u8f74\u8868\u793a\u4efb\u610f\u4e24\u4e2a\u8282\u70b9\u4e4b\u95f4\u6700\u77ed\u8ddd\u79bb\u7684\u5e73\u5747\u957f\u5ea6\u3002\u5982\u679cd\u5c0f\u8bf4\u660e\u4e24\u4e2a\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u7684\u9884\u671f\u957f\u5ea6\u8d8a\u5c0f\u3002<\/span><\/p>\n

      \n

      \u7406\u8bba\u7684\u65e0\u6807\u5ea6\u7f51\u7edc\u548c\u662f\u7684Internet\u7f51\u548c\u4e07\u7ef4\u7f51\u4e00\u6837\uff0c\u5728\u968f\u673a\u7684\u5931\u6548\u60c5\u51b5\u4e0b\u6781\u5177\u9c81\u68d2\u6027\uff0c\u4f46\u5728\u4e13\u95e8\u8fdb\u884c\u5927\u5ea6\u8282\u70b9\u653b\u51fb\u7684\u60c5\u51b5\u4e0b\u663e\u5f97\u5f88\u8106\u5f31\uff0c\u5e73\u5747\u6700\u77ed\u8ddd\u79bb\u5927\u5e45\u589e\u52a0<\/strong>\u3002\u800c\u968f\u673a\u7f51\u7edc\u5728\u8fd9\u4e24\u79cd\u60c5\u51b5\u4e0b\u8868\u73b0\u5f88\u4e00\u81f4\uff0c\u5e73\u5747\u6700\u77ed\u8ddd\u79bb\u4f1a\u968f\u7740\u79fb\u9664\u7684\u8282\u70b9\u589e\u52a0\u53ea\u662f\u6709\u5c0f\u5e45\u4e0a\u5347<\/strong>\u3002<\/span><\/p>\n

      \n

      \u65e0\u6807\u5ea6\u7f51\u7edc\u4e2d\u5927\u90e8\u5206\u7684\u8282\u70b9\u7684\u5ea6\u90fd\u5f88\u5c0f\uff0c\u5c5e\u4e8e\u201c\u53f6\u5b50\u201d\u8282\u70b9<\/span><\/strong>\uff0c\u5220\u9664\u5b83\u5bf9\u4e8e\u6574\u4e2a\u7f51\u7edc\u5f71\u54cd\u4e0d\u5927\uff0c\u4f46\u4e00\u65e6\u79fb\u9664\u6389\u5f88\u5927\u5ea6\u7684hub\u8282\u70b9\uff0c\u7f51\u7edc\u5c31\u4f1a\u53d8\u5f97\u4e00\u4e0b\u5b50\u96f6\u788e\uff0c\u6574\u4e2a\u7ed3\u6784\u88ab\u4e25\u91cd\u7834\u574f\u3002<\/span><\/p>\n

      \n

      \u8fd9\u4e2a\u7814\u7a76\u5177\u6709\u5e94\u7528\u4ef7\u503c\u3002\u5df2\u7ecf\u7814\u7a76\u53d1\u73b0\u4e00\u4e9b\u56fd\u5bb6\u7684\u822a\u7a7a\u7f51\u7edc\u5b83\u662f\u65e0\u6807\u5ea6\u7684<\/strong>\uff0c\u90a3\u4e48\u5728\u6218\u4e89\u7684\u65f6\u5019\u4e00\u65e6\u91cd\u8981\u673a\u573a\u88ab\u654c\u519b\u6467\u6bc1\uff0c\u6574\u4e2a\u56fd\u5bb6\u7684\u822a\u7a7a\u7f51\u7edc\u5c31\u5d29\u6e83\u4e86\u3002\u53e6\u5916\uff0c\u4e00\u4e9b\u5927V\u6563\u64ad\u8c23\u8a00\u5c31\u4f1a\u88ab\u7981\u8a00\uff0c\u5c31\u76f8\u5f53\u4e8e\u8fd9\u4e9b\u91cd\u8981\u7684\u8fd9\u4e9b\u8282\u70b9\u88ab\u79fb\u9664\uff0c\u90a3\u4e48\u6574\u4e2a\u7f51\u7edc\u5c31\u4f1a\u4ece\u8c23\u8a00\u6216\u8005\u662f\u4ece\u4e00\u4e9b\u4e0d\u826f\u4fe1\u606f\u7684\u4f20\u64ad\u91cc\u9762\u6062\u590d\u5230\u6b63\u5e38\u72b6\u6001\uff0c\u8fd9\u662f\u76ee\u524d\u793e\u4f1a\u6cbb\u7406\u4e2d\u7684\u4e00\u4e2a\u7814\u7a76\u5185\u5bb9\u3002<\/span><\/p>\n

      \n

      2.2.2 \u65e0\u6807\u5ea6\u7f51\u7edc\u4e0a\u6d41\u884c\u75c5\u4e0d\u53ef\u6839\u9664<\/span><\/strong><\/span><\/p>\n

      \n

      \u7ecf\u5178\u7684SIS\u6a21\u578b\u8ba8\u8bba\u4e86\u6613\u611f\u8005\u548c\u88ab\u611f\u67d3\u8005\u4e4b\u95f4\u7684\u8f6c\u6362\uff0c\u662f\u57fa\u4e8e\u5747\u5300\u6df7\u5408\u7684\u4eba\u7fa4\u7684\uff0c\u4e5f\u5c31\u662f\u4efb\u4f55\u4e24\u4e2a\u4eba\u90fd\u6709\u6f5c\u5728\u7684\u76f8\u540c\u7684\u6982\u7387\u76f8\u4e92\u611f\u67d3<\/strong>\u3002<\/span><\/p>\n

      \n

      \u5982\u679c\u6d41\u884c\u75c5\u7684\u4f20\u64ad\u662f\u901a\u8fc7\u65e0\u6807\u5ea6\u7f51\u7edc\u8fdb\u884c\u7684\uff0c\u7ed3\u679c\u4f1a\u8ba9\u4eba\u5403\u60ca\u3002\u56fe17\u8868\u660e\u5728\u5f88\u5c0f\u7684\u6709\u6548\u4f20\u67d3\u5f3a\u5ea6\u60c5\u51b5\u4e0b\uff0c\u4e0d\u540c\u89c4\u6a21\u7684\u65e0\u6807\u5ea6\u7f51\u7edc\u4e0a\u7684\u88ab\u611f\u67d3\u8282\u70b9\u7684\u5bc6\u5ea6\u53d8\u5316\uff0c\u5f53\u7f51\u7edc\u89c4\u6a21\u5f88\u5927\u7684\u65f6\u5019\uff0c\u88ab\u611f\u67d3\u8282\u70b9\u7684\u5bc6\u5ea6\u8870\u51cf\u5f88\u6162<\/strong>\u3002\u6570\u5b66\u5206\u6790\u8868\u660e\uff0c\u53ea\u6709\u5728\u7684\u60c5\u51b5\u4e0b\uff0c\u611f\u67d3\u5bc6\u5ea6\u624d\u4f1a\u8d8b\u8fd10\u3002\u4e5f\u5c31\u662f\u8bf4\u5728\u65e0\u6807\u5ea6\u7f51\u7edc\u4e0a\u4f20\u67d3\u75c5\u4e00\u822c\u662f\u4e0d\u80fd\u6839\u9664\u7684<\/strong>\u3002\u4e0d\u7ba1\u4f60\u4f20\u64ad\u5f3a\u5ea6\u5982\u4f55\u7684\u5c0f\uff0c\u4ee5\u53ca\u6cbb\u6108\u7684\u80fd\u529b\u591a\u4e48\u7684\u5927\uff0c\u90a3\u4e48\u8fd9\u4e00\u4e2a\u7f51\u7edc\u4e0a\u7684\u75c5\u6bd2\u662f\u4e0d\u53ef\u80fd\u6839\u9664\u7684\u3002<\/span><\/p>\n

      \n

      \u4f8b\u5982\u8ba1\u7b97\u673a\u75c5\u6bd2\u5728Internet\u7f51\u7edc\u4e0a\u5c31\u96be\u4ee5\u6839\u9664\u3002\u65e0\u8bba\u6740\u6bd2\u8f6f\u4ef6\u518d\u5f3a\uff0c\u53ea\u8981\u4e0d\u662f100%\u514d\u75ab\uff0c\u53ea\u8981\u5927\u5bb6\u90fd\u8054\u7f51\uff0c\u800c\u7f51\u7edc\u7684\u5ea6\u5206\u5e03\u670d\u4ece\u5e42\u5f8b\u5206\u5e03\uff0c\u90a3\u4e48\u5c31\u4e0d\u53ef\u80fd\u628a\u75c5\u6bd2\u4ece\u6574\u4e2a\u8ba1\u7b97\u673a\u7f51\u7edc\u4e0a\u6e05\u9664\u5e72\u51c0\uff0c\u53ea\u8981\u8ba1\u7b97\u673a\u5728\u7f51\u4e0a\uff0c\u5b83\u5c31\u6709\u88ab\u4f20\u67d3\u7684\u5371\u9669\u3002<\/span><\/p>\n

      \n

      \"\u96c6\u667a\"<\/p>\n

      \n

      \u56fe15 \u6d41\u884c\u75c5\u5728\u65e0\u6807\u5ea6\u7f51\u7edc\u4e0a\u7684\u5b58\u6d3b\u6982\u7387<\/strong><\/span><\/p>\n

      \u6570\u636e\u6765\u6e90\uff1aPastor-Satorras, R., & Vespignani, A.(2001). Epidemic spreading in scale-free networks.Physical review letters,86(14), 3200.<\/strong><\/span><\/p>\n

      \n

      \u4e86\u89e3\u65e0\u6807\u5ea6\u7f51\u7edc\u7684\u7279\u5f81\u4e4b\u540e\uff0c\u5c31\u53ef\u4ee5\u52a0\u4ee5\u5229\u7528\uff0c\u6bd4\u5982\u5728\u793e\u4f1a\u8206\u8bba\u4e0a\u6211\u4eec\u5982\u4f55\u53bb\u5f15\u5bfc\u6784\u5efa\u548c\u8c10\u7684\u8206\u8bba\u6c1b\u56f4\uff0c\u5bf9\u4e8e\u8fd9\u4e00\u4e9b\u5173\u952e\u7684\u8282\u70b9\u8be5\u600e\u4e48\u53bb\u5904\u7406\u5b83\uff0c\u4f8b\u5982\u8ba9\u4ed6\u4eec\u7ecf\u5e38\u53d1\u8868\u79ef\u6781\u5411\u4e0a\u7684\u89c2\u70b9\uff08\u6d41\u884c\u7684\u8bdd\u662f\u201c\u6b63\u80fd\u91cf\u201d\uff09\u65e0\u7591\u5bf9\u4e8e\u793e\u4f1a\u6cbb\u7406\u662f\u6709\u76ca\u7684\u3002\u4e3a\u4e86\u9632\u8303\u7cfb\u7edf\u6027\u91d1\u878d\u98ce\u9669\uff0c\u8981\u5148\u4e86\u89e3\u94f6\u884c\u4e4b\u95f4\u7684\u501f\u8d37\u5173\u7cfb\u6784\u5efa\u501f\u8d37\u7f51\u7edc\uff0c\u907f\u514d\u7ea7\u8054\u6548\u5e94\u9020\u6210\u7684\u5927\u89c4\u6a21\u94f6\u884c\u5012\u95ed\u3002<\/span><\/p>\n

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

      \n

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

      3.\u5982\u4f55\u4ea7\u751f\u5e42\u5f8b\u5206\u5e03<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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

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

      \u524d\u9762\u8c08\u4e86\u5e42\u5f8b\u5206\u5e03\u4ee5\u53ca\u5ea6\u5206\u5e03\u670d\u4ece\u5e42\u5f8b\u5206\u5e03\u7684\u65e0\u6807\u5ea6\u7f51\u7edc\uff0c\u4e0b\u9762\u8fd8\u6709\u4e24\u4e2a\u95ee\u9898\uff1a<\/span><\/p>\n

      1\u3001\u4ec0\u4e48\u673a\u5236\u4ea7\u751f\u5e42\u5f8b\u5206\u5e03\uff0c<\/span><\/strong><\/p>\n

      2\u3001\u5982\u4f55\u53bb\u4f30\u8ba1\u548c\u68c0\u9a8c\u4e00\u4e2a\u5b9e\u9645\u7684\u5206\u5e03\u3002<\/span><\/strong><\/p>\n

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

      \u80fd\u4ea7\u751f\u5e42\u5f8b\u5206\u5e03\u7684\u673a\u5236\u975e\u5e38\u591a\uff0c\u8fd9\u513f\u53ea\u7ed9\u51fa\u51e0\u4e2a\u7ecf\u5178\u3001\u6709\u8da3\u7684\u4f8b\u5b50\u3002<\/span><\/p>\n

      \n

      \n
      \n
      <\/p>\n

      3.1\u504f\u597d\u4f9d\u9644<\/strong><\/span><\/p>\n

      \uff08Preferential Attachment\uff09\u6a21\u578b<\/strong><\/span><\/p>\n

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

      \n

      Barabasi\u57281999\u5e74\u53d1\u8868\u7684\u6587\u7ae0\uff0c\u63d0\u51fa\u4e86\u8457\u540d\u7684\u504f\u597d\u4f9d\u9644\u6a21\u578b<\/span><\/strong>\uff0c\u8fd9\u662f\u4e00\u4e2a\u52a8\u6001\u7684\u7f51\u7edc\u751f\u957f\u6a21\u578b\uff0c\u6b65\u9aa4\u5982\u56fe16\u6240\u793a\uff0c\u521d\u59cb\u65f6\u5019\u7f51\u7edc\u4e0a\u5b58\u5728\u4e00\u4e9b\u8282\u70b9\u548c\u8fde\u8fb9\uff0c\u6bcf\u6b21\u589e\u52a0\u4e00\u4e2a\u8282\u70b9\u548c\u56fa\u5b9a\u7684\u8fb9\u6570\uff0c\u8fd9\u4e9b\u8fb9\u4e0d\u662f\u7b49\u6982\u7387\u627e\u4e24\u4e2a\u4ee5\u524d\u7684\u8282\u70b9\u8fde\u4e0a\uff0c\u800c\u662f\u4ee5\u8f83\u5927\u7684\u6982\u7387\u9009\u62e9\u5ea6\u6bd4\u8f83\u591a\u7684\u8282\u70b9<\/strong>\uff0c\u8fd9\u5c31\u662f\u504f\u597d\u4f9d\u9644\u7684\u601d\u60f3\u4f53\u73b0\uff0c\u6570\u5b66\u5f62\u5f0f\u4e0a\u53ef\u4ee5\u5199\u4e3a<\/span><\/p>\n

      \"\u96c6\u667a\" \uff087\uff09<\/p>\n

      \u8868\u793a\u8fde\u63a5\u5230\u5ea6\u4e3a\u7684\u8282\u70b9\u7684\u6982\u7387\u3002\u540e\u7eed\u5df2\u7ecf\u6709\u4e00\u4e9b\u7c7b\u4f3c\u7684\u673a\u5236\u4ea7\u751f\u4e0d\u540c\u6307\u6570\u7684\u65e0\u6807\u5ea6\u7f51\u7edc\u3002\u5728\u8fd9\u513f\u8981\u5f3a\u8c03\u4e00\u4e0b\u8fd9\u4e2a\u504f\u597d\u4f9d\u9644\u7684\u601d\u60f3\u5b9e\u9645\u4e0a\u662f\u6709\u5f88\u6df1\u7684\u610f\u4e49\uff0c\u9a6c\u592a\u6548\u5e94\u8bf4\u7684\u4e5f\u662f\u8fd9\u4e2a\u610f\u601d\uff0c\u6b63\u53cd\u9988\u4e5f\u662f\u8fd9\u4e2a\u610f\u601d<\/strong>\u3002\u73b0\u5b9e\u4e0a\u80fd\u627e\u5230\u5f88\u591a\u6b63\u53cd\u9988\u7684\u4f8b\u5b50\u6765\u8bf4\u660e\u5e42\u5f8b\u5206\u5e03\uff0c\u4f8b\u5982\u6709\u4e00\u7bc7\u6587\u7ae0\u63d0\u5230\uff0c\u5bf9\u4e8e\u540d\u5b57\u7684\u504f\u597d\u4f7f\u7528\u9020\u6210\u540d\u5b57\u7684\u5206\u5e03\u5448\u73b0\u5e42\u5f8b\u7279\u5f81<\/strong>\u3002<\/span><\/p>\n

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

      \"\u96c6\u667a\"<\/p>\n

      \u56fe16 \u504f\u597d\u4f9d\u9644\u7f51\u7edc\u7684\u5f62\u6210\u8fc7\u7a0b<\/span><\/strong><\/p>\n

      \u6570\u636e\u6765\u6e90\uff1ahttp:\/\/barabasi.com\/publications\/1\/review-articles<\/span><\/strong><\/p>\n

      \n

      \n
      \n
      <\/p>\n

      3.2 \u8d27\u5e01\u8f6c\u79fb\u6a21\u578b<\/strong><\/span><\/p>\n

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

      \u5728\u8ba8\u8bba\u6536\u5165\u548c\u8d22\u5bcc\u5206\u5e03\u7684\u65f6\u5019\uff0c\u4e00\u4e2a\u7ecf\u5178\u6a21\u578b\u5c31\u662f\u8d27\u5e01\u8f6c\u79fb\u6a21\u578b\u3002<\/span><\/strong>\u8fd9\u4e2a\u6a21\u578b\u5f88\u7b80\u5355\uff0c\u5982\u56fe17\u6240\u793a\uff0c\u5c31\u662f\u4e00\u5806\u4eba\u6765\u968f\u673a\u74dc\u5206\u4e00\u5806\u94b1\uff0c\u5728\u6a21\u578b\u7684\u8fd0\u884c\u8fc7\u7a0b\u4e2d\uff0c\u968f\u673a\u627e\u51fa\u4e24\u4e2a\u4eba\u8fdb\u884c\u4ea4\u6613\uff0c\u4ea4\u6613\u8fc7\u7a0b\u5c31\u662f\u628a\u4ed6\u4eec\u7684\u94b1\u653e\u4e00\u8d77\u518d\u505a\u4e00\u6b21\u968f\u673a\u5206\u914d\u3002\u8fd9\u4e2a\u56fe\u4e0a\u7684\u8fde\u7ebf\u8868\u793a\u4ea4\u6613\u5173\u7cfb\u3002\u5728\u4e0d\u540c\u7684\u53c2\u6570\u60c5\u51b5\u4e0b\u6a21\u578b\u4f1a\u5f97\u5230\u4e0d\u540c\u7684\u7ed3\u679c\u3002<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe17 \u8d27\u5e01\u8f6c\u79fb\u6a21\u578b\u793a\u610f\u56fe<\/span><\/strong><\/span><\/p>\n

      \n

      \u5047\u5982\u65f6\u523b\u7684\u4e24\u4e2a\u4e2a\u4f53\u624b\u4e2d\u7684\u8d27\u5e01\u5206\u522b\u4e3a\uff0c\u82e5\u4e8c\u4eba\u7684\u5b58\u50a8\u7387\u5206\u522b\u4e3a\uff0c\u5c31\u662f\u81ea\u5df1\u4fdd\u7559\u4e0b\u6765\u4e0d\u7528\u4e8e\u4ea4\u6613\u7684\u90e8\u5206\uff0c\u5219\u4e0b\u4e00\u65f6\u523b\u4e8c\u4eba\u7684\u8d27\u5e01\u6301\u6709\u91cf\u53d8\u4e3a<\/span><\/p>\n

      \"\u96c6\u667a\"\uff088\uff09<\/p>\n

      \u4ea4\u6613\u76f8\u5f53\u4e8e\u628a\u4e24\u4e2a\u4e2a\u4f53\u7684\u94b1\u6536\u96c6\u8d77\u6765\uff0c\u653e\u5728\u4e00\u4e2a\u5927\u7f50\u5b50\u91cc\u9762\u6447\u4e00\u6447\uff0c\u7136\u540e\u518d\u91cd\u65b0\u968f\u673a\u5206\u4e00\u4e0b\u7ed9\u4ed6\u4eec\u3002\u7136\u540e\u5927\u5bb6\u91cd\u65b0\u4e86\u94b1\uff0c\u518d\u53bb\u7b49\u5019\u4e0b\u4e00\u6b21\u4ea4\u6613\u3002\u6a21\u578b\u5728\u4e0d\u540c\u7684\u50a8\u84c4\u7387\u7684\u60c5\u51b5\u4e0b\u7ed3\u679c\u4e0d\u540c<\/strong>\uff0c\u5982\u679c\u50a8\u84c4\u7387\u4e3a0\uff0c\u5c31\u662f\u5927\u5bb6\u90fd\u628a\u94b1\u90fd\u62ff\u51fa\u6765\u968f\u673a\u5206\u914d\uff0c\u6700\u540e\u4e2a\u4f53\u7684\u6301\u5e01\u91cf\u7684\u5206\u5e03\u662f\u6307\u6570\u5206\u5e03\u3002\u800c\u5982\u679c\u5927\u5bb6\u6709\u4e00\u4e2a\u4e00\u6837\u4e0d\u4e3a0\u7684\u50a8\u84c4\u7387\uff0c\u6700\u540e\u4f1a\u5f97\u5230\u51fa\u4f3d\u9a6c\u5206\u5e03\u3002\u800c\u5982\u679c\u6bcf\u4e2a\u4e2a\u4f53\u7684\u50a8\u84c4\u7387\u4e0d\u540c\uff0c\u90fd\u662f\u968f\u673a\u7684\uff0c\u6700\u540e\u4f1a\u4ea7\u751f\u5e42\u5f8b\u5206\u5e03<\/strong>[3]\u3002<\/span><\/p>\n

      \n

      \n
      \n
      <\/p>\n

      3.3\u6700\u5c0f\u503c\u9650\u5236<\/strong><\/span><\/p>\n

      \u968f\u673a\u4e58\u6570\u6a21\u578b<\/strong><\/span><\/p>\n

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

      \n

      \u968f\u673a\u4e58\u6570\u6a21\u578b\u5982\u4e0b\u6240\u793a<\/span><\/p>\n

      \"\u96c6\u667a\" (9)<\/span><\/p>\n

      \u8868\u793a\u4e2a\u4f53\u7684\u5927\u5c0f\u662f\u5728\u8fed\u4ee3\u8fc7\u7a0b\u4e2d\u6bcf\u6b21\u4e58\u4ee5\u4e00\u4e2a\u968f\u673a\u6570\u4ea7\u751f\u7684\uff0c\u4f8b\u5982<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u5bf9\uff089\uff09\u53d6\u5bf9\u6570\u5e76\u8003\u8651\u5230\u957f\u671f\u4f5c\u7528\uff0c\u53ef\u5f97<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u6839\u636e\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\uff0clnX<\/em>\u7684\u6781\u9650\u884c\u4e3a\u662f\u6b63\u6001\u5206\u5e03\uff0c\u5373X<\/em><\/span>\u7684\u6781\u9650\u884c\u4e3a\u662f\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u3002\u5982\u679c\u5bf9\u968f\u673a\u4e58\u6570\u6a21\u578b\u589e\u52a0\u4e00\u4e2a\u5c0f\u7684\u8c03\u6574\uff0c\u8bbe\u5b9a\u4e00\u4e2a\u6700\u5c0f\u7684\u503c\uff0c\u5373\u5982\u679c<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u5219<\/span><\/p>\n

      \"\u96c6\u667a\"\uff0c<\/p>\n

      \u8fd9\u79cd\u5e26\u6709\u6700\u5c0f\u53cd\u5c04\u7684\u968f\u673a\u4e58\u6570\u6a21\u578b\u53ef\u4ee5\u5f97\u5230\u5e42\u5f8b\u5206\u5e03\u968f\u673a\u6570<\/span><\/strong>[4]\u3002<\/span><\/p>\n

      \n

      \n

      \n
      \n
      <\/p>\n

      3.4 \u7334\u5b50<\/strong><\/span><\/p>\n

      \u968f\u673a\u6253\u5b57\u6a21\u578b<\/strong><\/span><\/p>\n

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

      \u4e00\u4e9b\u5f88\u7b80\u5355\u7684\u673a\u5236\u53ef\u4ee5\u4ea7\u751f\u5e42\u5f8b\u5206\u5e03\u7684\u968f\u673a\u6570\u3002<\/span><\/strong>\u53eb\u4e00\u4e2a\u7334\u5b50\u6765\u7528\u4e00\u4e2a\u6709n\u4e2a\u5b57\u6bcd\u952e\u548c\u4e00\u4e2a\u7a7a\u683c\u952e\u7684\u952e\u76d8\u968f\u673a\u6253\u5b57\uff0c\u5047\u8bbe\u5b83\u4ee5\u6982\u7387p\u6572\u51fb\u7a7a\u683c\u952e\uff0c\u4ee51-p\u7684\u6982\u7387\u7b49\u53ef\u80fd\u7684\u6572\u51fbn\u4e2a\u5b57\u6bcd\u952e\u3002\u5219\u968f\u673a\u5f97\u5230\u4e00\u4e2a\u957f\u5ea6\u4e3ac\u7684\u5355\u8bcd\uff0c\u5b83\u5fc5\u987b\u8fde\u7eed\u6572\u51fbc\u6b21\u5b57\u6bcd\u952e\uff0c\u7136\u540e\u6309\u4e00\u6b21\u7a7a\u683c\u952e\uff0c\u6574\u4e2a\u8fc7\u7a0b\u5b9e\u73b0\u7684\u6982\u7387\u4e3a<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u5982\u679c\u6211\u4eec\u6309\u51fa\u6765\u7684\u8bcd\u9891\u4ece\u5927\u5230\u5c0f\u6392\u5e8f\uff0c\u968f\u673a\u51fa\u6765\u7684\u77ed\u7684\u8bcd\u80af\u5b9a\u6982\u7387\u5927\u4e00\u4e9b\uff0c\u4f1a\u6392\u524d\u9762\uff08\u7a7a\u683c\u662f\u4e00\u4e2a\u7279\u6b8a\u5355\u8bcd\uff0c\u5360\u636e\u4f4d\u7f6e1\uff09\uff0c\u5219\u6709\u957f\u5ea6\u4e3aj\u7684\u8bcd\u5360\u636e\u7684\u4f4d\u7f6e\u8303\u56f4\u662f<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u800c\u6392\u5e8f\u4f4d\u7f6e\u5927\u6982\u5728<\/span>\"\u96c6\u667a\"\u7684\u8bcd\u957f\u5ea6\u4e3aj\uff0c\u9891\u7387\u4e3a<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u4ee3\u5165<\/span>\"\u96c6\u667a\"\uff0c\u5c31\u53ef\u4ee5\u5f97\u5230<\/span><\/p>\n

      \"\u96c6\u667a\"\uff0810\uff09<\/span><\/p>\n

      \n

      \u5e42\u5f8b\u5206\u5e03\u7684\u4ea7\u751f\u673a\u5236\u8fd8\u6709\u975e\u5e38\u591a\uff0c\u5927\u5bb6\u6709\u5174\u8da3\u53ef\u4ee5\u81ea\u884c\u4e86\u89e3\u3002\u5982\u679c\u5bf9\u4e8e\u5e42\u5f8b\u5206\u5e03\u7684\u5e7f\u6cdb\u5b58\u5728\u611f\u5230\u597d\u5947\uff0c\u66f4\u5e94\u8be5\u4e86\u89e3\u5e7f\u4e49\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406<\/strong>\uff0c\u5927\u6982\u610f\u601d\u662f\u5728\u65b9\u5dee\u6709\u9650\u7684\u60c5\u51b5\u4e0b\u591a\u4e2a\u72ec\u7acb\u4f5c\u7528\u7684\u6548\u679c\u7684\u6781\u9650\u662f\u6b63\u6001\u5206\u5e03\uff0c\u4f46\u5982\u679c\u65b9\u5dee\u65e0\u9650\u7684\u65f6\u5019\uff0c\u6781\u9650\u884c\u4e3a\u662fLevy\u7a33\u5b9a\u5206\u5e03\uff0c\u800c\u8fd9\u79cd\u5206\u5e03\u867d\u7136\u6ca1\u6709\u660e\u786e\u7684\u5bc6\u5ea6\u51fd\u6570\u5f62\u5f0f\uff0c\u4f46\u5c3e\u7aef\u53ef\u4ee5\u7528\u5e42\u5f8b\u5206\u5e03\u63cf\u8ff0\u3002\u5177\u4f53\u53ef\u4ee5\u53c2\u8003\u5317\u5e08\u5927\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u5f20\u6c5f\u8001\u5e08\u7684\u6587\u7ae0[5]\u3002<\/span><\/p>\n

      \n

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

      \n

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

      4.\u5982\u4f55\u4f30\u8ba1<\/span><\/strong><\/p>\n

      \u548c\u5224\u65ad\u5e42\u5f8b\u5206\u5e03<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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

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

      \u5224\u65ad\u5b9e\u9645\u73b0\u8c61\u662f\u5426\u670d\u4ece\u5e42\u5f8b\u5206\u5e03\u4ee5\u53ca\u4f30\u8ba1\u8fd9\u4e2a\u5e42\u5f8b\u6307\u6570\u662f\u5e94\u7528\u7684\u57fa\u7840\u3002<\/span><\/strong>\u8bd5\u60f3\u4e00\u4e2a\u793e\u4f1a\u5173\u7cfb\u7f51\u7edc\u662f\u4e00\u4e2a\u968f\u673a\u7f51\u7edc\uff0c\u4f46\u88ab\u8bef\u5224\u4e3a\u65e0\u6807\u5ea6\u7f51\u7edc\uff0c\u88ab\u5e94\u7528\u8fdb\u884c\u793e\u4f1a\u6cbb\u7406\u7b49\u65b9\u6cd5\uff0c\u7ed3\u679c\u4e0d\u4ec5\u6d6a\u8d39\u8d44\u6e90\u548c\u6210\u672c\uff0c\u8fd8\u53ef\u80fd\u9002\u5f97\u5176\u53cd\u3002\u5bf9\u5e42\u5f8b\u5206\u5e03\u7684\u4f30\u8ba1\u548c\u68c0\u9a8c\u4e3b\u8981\u4e3b\u8981\u662f\u4ece\u7ecf\u5178\u7684\u56de\u5f52+\u51b3\u5b9a\u7cfb\u6570\u5411\u6781\u5927\u4f3c\u7136\u4f30\u8ba1+KS\u68c0\u9a8c\u8f6c\u53d8\u3002<\/strong><\/span><\/p>\n

      \n

      \n

      \n
      \n
      <\/p>\n

      4.1\u56de\u5f52\u4e0e\u51b3\u5b9a\u7cfb\u6570<\/strong><\/span><\/p>\n

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

      \u5982\u679c\u6211\u4eec\u77e5\u9053\u5206\u5e03\u51fd\u6570\u7684\u5f62\u5f0f\uff0c\u901a\u8fc7\u76f4\u65b9\u56fe\u5c31\u53ef\u4ee5\u76f4\u63a5\u8fdb\u884c\u975e\u7ebf\u6027\u56de\u5f52<\/span><\/strong>\uff0c\u56fe18\u662f\u6211\u4eec\u5bf9\u4e8e\u4e00\u4e9b\u968f\u673a\u6570\u5f97\u5230\u7684\u76f4\u65b9\u56fe\u8fdb\u884c\u5e42\u51fd\u6570\u56de\u5f52\u7684\u7ed3\u679c\uff0c\u4f7f\u7528\u5de5\u5177\u4e3aorigin 8\u3002\u53ef\u4ee5\u76f4\u63a5\u5f97\u5230\u53c2\u6570\u7684\u4f30\u8ba1\u7f6e\u4fe1\u533a\u95f4\uff08\u4e00\u822c\u662f95%\uff09\u548c\u8bf4\u660e\u62df\u5408\u6548\u679c\u7684\u51b3\u5b9a\u7cfb\u6570R2\u3002\u5982\u679c\u51b3\u5b9a\u7cfb\u6570\u5927\uff0c\u8bf4\u660e\u7528\u5e42\u5f8b\u5206\u5e03\u51fd\u6570\u62df\u5408\u662f\u5408\u9002\u7684\u3002\u8fd9\u513f\u91c7\u7528\u7684\u6700\u5c0f\u4e8c\u4e58\u6cd5\u62df\u5408\u662f\u4f7f\u5f97\u6b8b\u5dee\u7684\u5e73\u65b9\u548c\u6700\u5c0f\u3002<\/span><\/p>\n

      \n

      \"\u96c6\u667a\"<\/p>\n

      \u56fe18 \u5bf9\u5e42\u5f8b\u5206\u5e03\u7684\u975e\u7ebf\u6027\u56de\u5f52<\/span><\/strong><\/span><\/p>\n

      \n

      \u975e\u7ebf\u6027\u62df\u5408\u7684\u8ba1\u7b97\u96be\u5ea6\u6bd4\u8f83\u5927\uff0c\u66f4\u5e7f\u6cdb\u7684\u4f7f\u7528\u662f\u5bf9\u6570\u7ebf\u6027\u56de\u5f52\u3002\u5373<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u56de\u5f52\u540e\u540c\u6837\u5f97\u5230\u53c2\u6570\u7684\u4f30\u8ba1\u548c\u51b3\u5b9a\u7cfb\u6570\u3002\u5982\u679c\u53ea\u662f\u77e5\u9053\u5927\u5c0f\u548c\u6392\u5e8f\u7684\u5173\u7cfb\uff0c\u53ef\u4ee5\u7528<\/span><\/p>\n

      \"\u96c6\u667a\"<\/p>\n

      \u6765\u8fdb\u884c\u56de\u5f52\u5f97\u5230\u4f30\u8ba1\uff0c\u7136\u540e\u6839\u636e\u5173\u7cfb\u6298\u7b97\u8fc7\u53bb<\/span>\"\u96c6\u667a\"\u3002\u4f46\u4e00\u4e9b\u7814\u7a76\u53d1\u73b0\u76f4\u63a5\u8fd9\u6837\u56de\u5f52\u5728\u6837\u672c\u91cf\u4e0d\u591a\u7684\u65f6\u5019\u5bb9\u6613\u51fa\u73b0\u504f\u5dee\uff0c\u800c\u5efa\u8bae\u4f7f\u7528<\/span><\/p>\n

      \"\u96c6\u667a\" \uff0811\uff09<\/p>\n

      \u4f5c\u8005[6]\u8ba4\u4e3a\u5bf9\u4e8e\u6392\u5e8f\u8c03\u65740.5\u540e\u7684\u4f30\u8ba1\u503c\u66f4\u52a0\u53ef\u9760\uff0c\u6b64\u65f6\u7684\u6807\u51c6\u5dee\u4e3a<\/span>\"\u96c6\u667a\"\uff0cn\u4e3a\u6837\u672c\u6570\u91cf\u3002<\/span><\/p>\n

      \n

      \n
      \n
      <\/p>\n

      4.2\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u4e0eKS\u68c0\u9a8c<\/strong><\/span><\/p>\n

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

      \u5bf9\u4e8e\u5e42\u5f8b\u5206\u5e03\u53c2\u6570\u7684\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u53ef\u4ee5\u53c2\u80032005\u5e74[7]\u548c2009\u5e74[8]Newman\u4ed6\u4eec\u7684\u6587\u7ae0\u3002\u8fd9\u513f\u53ea\u662f\u7b80\u8981\u8bf4\u4e00\u4e0b\u601d\u60f3\u3002\u6781\u5927\u4f3c\u7136\u7684\u601d\u60f3\u5c31\u662f\u8bf4\u80fd\u770b\u89c1\u7684\u8fd9\u4e9b\u6837\u672c\uff0c\u5c31\u662f\u56e0\u4e3a\u4f60\u770b\u89c1\u8fd9\u4e9b\u6837\u672c\u51fa\u73b0\u7684\u6982\u7387\u6700\u5927\u3002<\/strong>\u4e3a\u4e86\u65b9\u4fbf\u8ba1\u7b97\uff0c\u4e00\u822c\u5148\u7b97\u5bf9\u6570\u4f3c\u7136\u51fd\u6570\uff0c\u5728\u5bf9\u53c2\u6570\u6c42\u504f\u5bfc\uff0c\u83b7\u5f97\u53c2\u6570\u7684\u4f30\u8ba1\u3002<\/span><\/p>\n

      \n

      \u56de\u5230\u5e42\u5f8b\u5206\u5e03\u68c0\u9a8c\uff0c\u4ee5\u524d\u4e3b\u8981\u662f\u901a\u8fc7\u6700\u5c0f\u4e8c\u4e58\u6cd5\u5f97\u5230\u7684R2\u6765\u8fdb\u884c\u68c0\u9a8c\uff0c\u4e00\u822c\u51b3\u5b9a\u7cfb\u6570\u8d8a\u5927\u5c31\u8bf4\u660e\u7406\u8bba\u5206\u5e03\u7b26\u5408\u5f97\u5f88\u597d\uff0c\u4f46\u591a\u5c11\u624d\u7b97\u597d\u96be\u4ee5\u5224\u65ad\uff0c\u5927\u5bb6\u5bf9\u4e8e\u51b3\u5b9a\u7cfb\u6570\u7684\u4e34\u754c\u503c\u7b49\u4fe1\u606f\u96be\u4ee5\u8ba1\u7b97\u6216\u8005\u83b7\u5f97\u3002\u76ee\u524d\u5b66\u672f\u4e0a\u6bd4\u8f83\u5e38\u7528\u7684\u68c0\u9a8c\u662fKS\uff08Kolmogorov-Smirnov\uff09\u68c0\u9a8c\u3002<\/strong><\/span><\/p>\n

      \n

      KS\u68c0\u9a8c\u5e7f\u6cdb\u8fd0\u7528\u4e8e\u6bd4\u8f83\u4e00\u4e2a\u9891\u7387\u5206\u5e03f(x)\u4e0e\u7406\u8bba\u5206\u5e03g(x)\u6216\u8005\u4e24\u4e2a\u89c2\u6d4b\u503c\u5206\u5e03\u7684\u68c0\u9a8c\u65b9\u6cd5\u3002\u5176\u539f\u5047\u8bbeH0:\u4e24\u4e2a\u6570\u636e\u5206\u5e03\u4e00\u81f4\u6216\u8005\u6570\u636e\u7b26\u5408\u7406\u8bba\u5206\u5e03\u3002D=max| f(x)- g(x)|\uff0c\u5f53\u5b9e\u9645\u89c2\u6d4b\u503cD>D(n,\u03b1)\u5219\u62d2\u7eddH0\uff0c\u5426\u5219\u5c31\u4e0d\u62d2\u7eddH0\u5047\u8bbe\u3002<\/span><\/p>\n

      \n

      \u5982\u56fe\u662f\u4e24\u4e2a\u7d2f\u8ba1\u5206\u5e03\u51fd\u6570\uff0c\u4e00\u4e2a\u662f\u7406\u8bba\u7684\u4e00\u4e2a\u662f\u5b9e\u9645\u6570\u636e\u7684\uff0c\u627e\u5230\u4e24\u4e2a\u5206\u5e03\u7684\u6700\u5927\u95f4\u8dddD\u540e\u901a\u8fc7\u67e5\u8868\u5c31\u53ef\u4ee5\u8fdb\u884c\u5224\u65ad\uff0c\u5982\u679cD\u8d85\u51fa\u4e00\u5b9a\u663e\u8457\u6027\u6c34\u5e73\u4e0b\u7684\u4e34\u754c\u503c\u5c31\u62d2\u7edd\u5b9e\u9645\u6570\u636e\u7b26\u5408\u7406\u8bba\u5206\u5e03\u7684\u539f\u5047\u8bbe<\/strong>\u3002\u8fd9\u4e2a\u4e34\u754c\u503c\u8868\u4f1a\u56e0\u4e3a\u7406\u8bba\u5206\u5e03\u548c\u6837\u672c\u6570\u91cf\u800c\u4e0d\u4e00\u6837\uff0c\u5982\u679c\u4e0d\u65b9\u4fbf\u627e\u5230\u8fd9\u79cd\u4e34\u754c\u503c\u8868\u8fd8\u53ef\u4ee5\u4f7f\u7528\u8ba1\u7b97\u673a\u6a21\u62df\u751f\u6210\u968f\u673a\u6570\u8fdb\u884c\u591a\u6b21\u5b9e\u9a8c\u8ba1\u7b97\u8fdb\u884c\uff0c\u5177\u4f53\u4e5f\u53ef\u4ee5\u53c2\u8003Newman\u7b49\u4eba2009\u5e74\u7684\u6587\u7ae0\u3002<\/span><\/p>\n

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

      \"\u96c6\u667a\"<\/p>\n

      \n

      \u76ee\u524d\uff0c\u53ef\u4ee5\u76f4\u63a5\u4ece\u7f51\u7ad9\u83b7\u5f97\u6709\u5173\u4e8e\u5e42\u5f8b\u5206\u5e03\u968f\u673a\u6570\u751f\u6210\u3001\u5e42\u5f8b\u53c2\u6570\u4f30\u8ba1\u548c\u5e42\u5f8b\u5206\u5e03\u68c0\u9a8c\u7684\u7a0b\u5e8f<\/strong>\uff0c\u5305\u62ecR\u8bed\u8a00\u7684\u548cMatlab\u7684\u4ee5\u53caPython\u7684\uff0c\u4e0b\u8f7d\u5730\u5740\u662fhttp:\/\/tuvalu.santafe.edu\/~aaronc\/powerlaws\/\u3002<\/span><\/p>\n

      \n

      \u53c2\u8003\u6587\u732e<\/span><\/p>\n

      \n

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

      \n
      \n
      \n

      [1] Hardy, M. (2010). Pareto\u2019s law.The Mathematical Intelligencer,32(3),38-43.<\/span><\/p>\n

      [2] https:\/\/www.barabasilab.com\/post\/love-is-all-you-need<\/span><\/p>\n

      [3] Repetowicz, P., Hutzler, S., & Richmond, P. (2005). Dynamics ofmoney and income distributions.Physica A: Statistical Mechanics and its Applications,356(2-4), 641-654.<\/span><\/p>\n

      [4] Mitzenmacher, M. (2004). A brief history of generative models forpower law and lognormal distributions.Internet mathematics,1(2),226-251.<\/span><\/p>\n

      [5] http:\/\/swarmagents.cn.13442.m8849.cn\/files\/jake2011616211724.pdf<\/span><\/p>\n

      [6] Gabaix, X., & Ibragimov, R. (2011). Rank\u2212 1\/2: a simple way to improve the OLS estimation of tailexponents.Journal of Business & Economic Statistics,29(1),24-39.<\/span><\/p>\n

      [7] Newman, M. E. (2005). Power laws, Pareto distributions and Zipf’slaw.Contemporary physics,46(5), 323-351.<\/span><\/p>\n

      [8] Clauset, A., Shalizi, C. R., & Newman, M.E. (2009). Power-law distributions in empirical data.SIAM review,51(4),661-703.<\/span><\/p>\n

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

      \n

      \n
      \n
      \n

      \u7f16\u8f91\uff1a\u738b\u6021\u853a<\/span><\/p>\n<\/blockquote>\n

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

      \n
      \"\u96c6\u667a\"<\/div>\n

      \n

      \n
      \n
      \n
      \n
      \n
      \n

      \u96c6\u667a\u4ff1\u4e50\u90e8QQ\u7fa4\uff5c877391004<\/span><\/strong><\/p>\n

      \u5546\u52a1\u5408\u4f5c\u53ca\u6295\u7a3f\u8f6c\u8f7d\uff5cswarma@swarma.org<\/span><\/strong><\/p>\n

      \n

      \u25c6<\/span>\u25c6<\/span>\u25c6<\/span><\/span><\/strong><\/strong><\/h1>\n<\/section>\n

      \u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/span><\/strong><\/span><\/p>\n

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

      \u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/span><\/strong><\/span><\/p>\n

      \n
      \"\u96c6\u667a\"<\/div>\n<\/section>\n

      \u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

      \n

      \u539f\u6587\u59cb\u53d1\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7\uff08 \u96c6\u667a\u4ff1\u4e50\u90e8 \uff09\uff1a\u96c6\u667a<\/a><\/p>\n<\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

      \u660e\u65e5\u7ebf\u4e0a\u516c\u5f00\u8bfe\u9884\u544a \u60f3\u8981\u66f4\u597d\u5730\u4e86\u89e3\u5e42\u5f8b\u5206\u5e03\uff0c \u4e0b\u9762\u8fd9\u8282\u514d\u8d39\u516c\u5f00\u8bfe\u600e\u4e48\u80fd\u9519\u8fc7\uff1f\uff01 10\u670810\u65e5 19:00-20:30 \u5e26\u4f60\u542f\u7a0b \u672c\u6587\u4ecb\u7ecd\u4e86\u5e42\u5f8b\u5206\u5e03\u7684\u5f62\u5f0f\u3001\u7279\u70b9\u4ee5\u53ca\u65e0\u6807\u5ea6\u7f51\u7edc\u7684\u5f62\u5f0f\u548c\u7279\u70b9\uff0c\u7279\u522b\u662f\u65e0\u6807\u5ea6\u7f51\u7edc\u5728\u4e8e\u62b5\u5fa1\u653b\u51fb\u548c\u4f20\u67d3\u75c5\u4f20\u64ad\u4e0a\u7684\u7279\u5f02\u6027\u3002\u5217\u4e3e\u4e86\u4e00\u4e9b\u7ecf\u5178\u7684\u5e42\u5f8b\u5206\u5e03\u968f\u673a\u53d8\u91cf\u751f\u6210\u673a\u5236\uff0c\u6700\u540e\u7b80\u4ecb\u4e86\u5bf9\u6570\u7ebf\u6027\u56de…<\/p>\n","protected":false},"author":1,"featured_media":11825,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[18],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/11823"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11823"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/11823\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/11825"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11823"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11823"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11823"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=11823"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}