{"id":39623,"date":"2023-01-03T22:44:41","date_gmt":"2023-01-03T14:44:41","guid":{"rendered":"https:\/\/swarma.org\/?p=39623"},"modified":"2023-01-03T22:44:41","modified_gmt":"2023-01-03T14:44:41","slug":"nat-commun-%e7%bb%bc%e8%bf%b0%ef%bc%9a%e7%bb%9f%e8%ae%a1%e6%8e%a8%e6%96%ad%e6%80%8e%e6%a0%b7%e8%bf%9e%e9%80%9a%e7%bd%91%e7%bb%9c%e7%a7%91%e5%ad%a6%e4%b8%ad%e7%9a%84%e6%95%b0%e6%8d%ae%e4%b8%8e","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=39623","title":{"rendered":"Nat. Commun.\u7efc\u8ff0\uff1a\u7edf\u8ba1\u63a8\u65ad\u600e\u6837\u8fde\u901a\u7f51\u7edc\u79d1\u5b66\u4e2d\u7684\u6570\u636e\u4e0e\u7406\u8bba"},"content":{"rendered":"
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Leto Peel, Tiago P. Peixoto & Manlio De Domenico<\/span> <\/span>| <\/strong><\/span>\u4f5c\u8005<\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n

\u5218\u5fd7\u822a<\/span> <\/span>| <\/strong><\/span>\u8bd1\u8005<\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/p>\n

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Statistical inference links data and theory in network science<\/span><\/p>\n

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\u4e00\u4e2a\u5178\u578b\u7684\u4f8b\u5b50\u662f Zachary \u7684\u7a7a\u624b\u9053\u4ff1\u4e50\u90e8\u7f51\u7edc\uff0c\u5b83\u4ee3\u8868\u4e86\u4e00\u4e2a\u7a7a\u624b\u9053\u4ff1\u4e50\u90e8\u7684\u6210\u5458\u4e4b\u95f4\u7684\u793e\u4ea4\u4e92\u52a8[38]\u3002\u8fd9\u4e2a\u7f51\u7edc\u662f\u53d1\u5c55\u7f51\u7edc\u79d1\u5b66\u65b9\u6cd5\u7684\u6700\u7b80\u5355\u548c\u6700\u5e7f\u6cdb\u4f7f\u7528\u7684\u793e\u4f1a\u7f51\u7edc\u4e4b\u4e00\uff0c\u6700\u5e38\u88ab\u7528\u4f5c\u6807\u51c6\u6d4b\u8bd5\u7f51\u7edc\uff0c\u800c\u4e0d\u662f\u4f5c\u4e3a\u7814\u7a76\u5bf9\u8c61\u3002\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u8bba\u6587\u4e2d\u4e00\u4e2a\u660e\u663e\u7684\u8f6c\u5f55\u9519\u8bef\uff0c\u5b83\u59a8\u788d\u4e86\u5bf9\u6570\u636e\u8fdb\u884c\u5b8c\u5168\u660e\u786e\u7684\u8ba1\u7b97\uff1a\u8bb0\u5f55\u7684\u90bb\u63a5\u77e9\u9635\u5305\u542b\u4e00\u4e2a\u53ef\u8bc1\u660e\u7684\u9519\u8bef\uff0c\u56e0\u4e3a\u6761\u76ee\uff0823,34\uff09\u4e3a\u96f6\uff0c\u800c\u6761\u76ee\uff0834,23\uff09\u4e3a\u975e\u96f6\uff0c\u5c3d\u7ba1\u8be5\u7f51\u7edc\u662f\u65e0\u5411\u7684\u3002\u8fd9\u79cd\u6a21\u7cca\u6027\u5728\u539f\u8bba\u6587\u4e2d\u63d0\u51fa\u7684\u77e9\u9635\u7684\u52a0\u6743\u548c\u975e\u52a0\u6743\u7248\u672c\u4e2d\u90fd\u4f1a\u51fa\u73b0\u3002\u6b64\u5916\uff0c\u5373\u4f7f\u4eba\u4e0e\u4eba\u4e4b\u95f4\u7684\u4e92\u52a8\u88ab Zachary \u5b8c\u6574\u65e0\u8bef\u5730\u624b\u5de5\u8bb0\u5f55\u4e0b\u6765\uff0c\u7814\u7a76\u754c\u4e5f\u65e0\u6cd5\u83b7\u5f97\u57fa\u672c\u7684\u539f\u59cb\u6570\u636e<\/span>\uff08\u76f4\u63a5\u89c2\u5bdf\u3001\u8c03\u67e5\u3001\u5b66\u6821\u8bb0\u5f55\uff09<\/span>\u4ee5\u53ca\u76f8\u5173\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u8fd9\u79cd\u57fa\u672c\u6d4b\u91cf\u4fe1\u606f\u7684\u7f3a\u4e4f\uff0c\u4e25\u91cd\u9650\u5236\u4e86\u6700\u7ec8\u80fd\u4ece\u8fd9\u4e9b\u6570\u636e\u4e2d\u4e86\u89e3\u5230\u7684\u60c5\u51b5\u3002<\/span><\/section>\n

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<\/section>\n
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\u8fd9\u79cd\u8282\u70b9\u7684\u4e0d\u786e\u5b9a\u6027\u5728\u7f51\u7edc\u79d1\u5b66\u6587\u732e\u4e2d\u8fd8\u6ca1\u6709\u771f\u6b63\u5f97\u5230\u8db3\u591f\u7684\u91cd\u89c6\u3002\u7136\u800c\uff0c\u89e3\u51b3\u8fd9\u4e9b\u4e0d\u786e\u5b9a\u6027\u4e4b\u524d\u5df2\u7ecf\u5728\u4e0d\u540c\u6570\u636e\u6e90\u7684\u5b9e\u4f53\u5339\u914d\u65b9\u9762\u8fdb\u884c\u4e86\u63a2\u7d22[55,56]\u3002\u8fd9\u4e2a\u95ee\u9898\u901a\u5e38\u88ab\u79f0\u4e3a\u5b9e\u4f53\u89e3\u6790\uff0c\u4f46\u4e5f\u6709\u5176\u4ed6\u540d\u79f0\uff0c\u5982\u8bb0\u5f55\u94fe\u63a5\u3001\u91cd\u590d\u6570\u636e\u5220\u9664\u3001\u5bf9\u8c61\u8bc6\u522b\u548c\u8eab\u4efd\u4e0d\u786e\u5b9a\u6027\u7b49\u7b49\u3002\u867d\u7136\u8fd9\u4e2a\u9886\u57df\u7684\u5f88\u591a\u5de5\u4f5c\u6ca1\u6709\u5e94\u7528\u4e8e\u6211\u4eec\u901a\u5e38\u8868\u793a\u4e3a\u7f51\u7edc\u7684\u6570\u636e\uff0c\u4f46\u662f\u540e\u6765\u7684\u5de5\u4f5c\u5229\u7528\u4e86\u7f51\u7edc\u7ed3\u6784\uff0c\u4ee5\u6539\u5584\u5339\u914d[57-59]\u3002<\/span><\/section>\n

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4. \u8868\u793a\u65b9\u6cd5\u7684\u9009\u62e9<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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 <\/span><\/section>\n
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\u6211\u4eec\u5f3a\u8c03\uff0c\u5bf9\u4e8e\u4efb\u4f55\u7279\u5b9a\u7684\u6570\u636e\u6765\u8bf4\uff0c\u6ca1\u6709\u56fa\u6709\u7684\u6b63\u786e\u7684\u7f51\u7edc\u8868\u793a\uff0c\u8fd9\u5b8c\u5168\u53d6\u51b3\u4e8e\u6240\u5bfb\u6c42\u7684\u7b54\u6848\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5728\u4f20\u67d3\u75c5\u7684\u4f20\u64ad\u7814\u7a76\u4e2d\uff0c\u4e34\u8fd1\u7f51\u7edc\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5f88\u597d\u7684\u8868\u793a\u65b9\u6cd5\uff0c\u4f8b\u5982\uff0c\u5b83\u4e3b\u8981\u4f9d\u8d56\u4e8e\u8eab\u4f53\u63a5\u89e6\u7684\u65f6\u95f4\u548c\u4e34\u8fd1\u7a0b\u5ea6\uff0c\u800c\u4e0d\u4f9d\u8d56\u4e8e\u662f\u4ec0\u4e48\u4fc3\u6210\u4e86\u8fd9\u79cd\u4e34\u8fd1\u3002\u7cbe\u5fc3\u8bbe\u8ba1\u7684\u53d7\u63a7\u5b9e\u9a8c\u4e2d\uff0c\u7cbe\u5fc3\u9009\u62e9\u548c\u6821\u51c6\u7684\u4e2a\u4eba\u4f20\u611f\u5668\uff0c\u4ee5\u68c0\u6d4b\u76f8\u5173\u7269\u7406\u548c\u65f6\u95f4\u8303\u56f4\u5185\u7684\u63a5\u8fd1\u7a0b\u5ea6\uff0c\u5df2\u88ab\u7528\u4e8e\u91cd\u6784\u6f5c\u5728\u7684\u4f20\u64ad\u9014\u5f84\u7f51\u7edc\uff0c\u5e76\u7814\u7a76\u51cf\u8f7b\u4f20\u67d3\u7684\u7b56\u7565\u7684\u6548\u679c[75-83]\u3002\u7136\u800c\uff0c\u5373\u4f7f\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6240\u9009\u62e9\u7684\u7f51\u7edc\u8868\u5f81\u662f\u4ee4\u4eba\u4fe1\u670d\u7684\uff0c\u4eba\u4eec\u4ecd\u7136\u9700\u8981\u8003\u8651\u5728\u4f55\u79cd\u7a0b\u5ea6\u4e0a\u53ef\u4ee5\u4ece\u6570\u636e\u4e2d\u63d0\u53d6\u3002\u4f7f\u7528\u5f02\u8d28\u6216\u672a\u6821\u51c6\u7684\u8bbe\u5907\uff0c\u4ee5\u53ca\u73af\u5883\u6548\u5e94<\/span>\uff08\u7269\u4f53\u3001\u5899\u58c1\u3001\u5730\u677f\u7b49\u7684\u5438\u6536\/\u53cd\u5c04\uff09<\/span>\u6269\u5927\u4e86\u68c0\u6d4b\u5230\u7684\u63a5\u8fd1\u4e8b\u4ef6\u548c\u6f5c\u5728\u4f20\u8f93\u4e4b\u95f4\u7684\u5dee\u8ddd[84]\u3002\u9002\u5f53\u5730\u9009\u62e9\u8868\u793a\u65b9\u6cd5\u6c38\u8fdc\u4e0d\u4f1a\u6d88\u9664\u5bf9\u63a8\u65ad\u6b65\u9aa4\u7684\u9700\u8981\uff0c\u8be5\u6b65\u9aa4\u4ece\u6570\u636e\u4e2d\u63d0\u53d6\u611f\u5174\u8da3\u7684\u57fa\u672c\u5bf9\u8c61\uff0c\u5177\u6709\u4e00\u5b9a\u7684\u4e0d\u786e\u5b9a\u6027\u3002<\/span><\/section>\n

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\uff08III\uff09\u57fa\u4e8e\u5177\u4f53\u7c92\u5ea6\u89c4\u5b9a\u7684\u91cd\u6784\u3002<\/strong>\u4e3a\u5206\u6790\u9009\u62e9\u76f8\u5173\u7684\u65f6\u95f4\u6216\u7a7a\u95f4\u5c3a\u5ea6\uff0c\u4e5f\u79f0\u4e3a\u7c97\u7c92\u5ea6\uff0c\u662f\u5404\u79cd\u5e94\u7528\u5b66\u79d1<\/span>\uff08\u4e0d\u4ec5\u4ec5\u662f\u7f51\u7edc\u79d1\u5b66\uff09<\/span>\u9700\u8981\u89e3\u51b3\u7684\u53e6\u4e00\u4e2a\u65e0\u5904\u4e0d\u5728\u7684\u56f0\u96be\u95ee\u9898\u3002\u4e00\u4e2a\u7ed9\u5b9a\u7684\u5c3a\u5ea6\u9009\u62e9\uff0c\u6216\u7cfb\u7edf\u4e2d\u88ab\u6d4b\u91cf\u7684\u65b9\u9762\uff0c\u5c06\u4e0d\u53ef\u907f\u514d\u5730\u63a9\u76d6\u8f83\u5c0f\u5c3a\u5ea6\u7684\u4fe1\u606f\uff0c\u6216\u672a\u88ab\u6d4b\u91cf\u7684\u65b9\u9762\u3002\u56e0\u6b64\uff0c\u57fa\u4e8e\u7279\u5b9a\u9009\u62e9\u7684\u76f4\u63a5\u7f51\u7edc\u8868\u793a\u53ef\u80fd\u53ea\u63d0\u4f9b\u4e86\u6574\u4e2a\u7cfb\u7edf\u7684\u4e0d\u5b8c\u6574\u6216\u626d\u66f2\u7684\u753b\u9762\u3002<\/span><\/section>\n

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<\/section>\n
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<\/section>\n
\uff08V\uff09\u57fa\u4e8e\u5bf9\u6270\u52a8\u7684\u53cd\u5e94\u7684\u91cd\u6784\u3002<\/strong>\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u4eba\u4eec\u89c2\u5bdf\u4e00\u4e2a\u7cfb\u7edf\u5355\u4f4d\u7684\u65f6\u95f4\u8fc7\u7a0b\uff0c\u4f46\u4e5f\u6709\u673a\u4f1a\uff1a\uff08i\uff09\u7528\u5c0f\u7684\u6270\u52a8\u4f5c\u7528\u4e8e\u7cfb\u7edf\u5e76\u8bb0\u5f55\u5176\u52a8\u6001\u54cd\u5e94\uff0c\u6216\u8005\uff08ii\uff09\u83b7\u53d6\u5df2\u77e5\u6270\u52a8\u53d1\u751f\u5728\u7a7a\u95f4\u548c\u65f6\u95f4\u7684\u7279\u5b9a\u70b9\u7684\u6570\u636e\u3002<\/span><\/section>\n

<\/section>\n
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<\/section>\n
\u5bf9\u4e8e\u7279\u5b9a\u7c7b\u578b\u7684\u52a8\u529b\u5b66<\/span>\uff08\u4f8b\u5982\uff0c\u6d41\u884c\u75c5\u4f20\u64ad\u6216\u4fe1\u606f\u6269\u6563\uff09<\/span>\uff0c\u6270\u52a8\u53ef\u4ee5\u5728\u6bcf\u4e2a\u65f6\u95f4\u6b65\u9aa4\u4e2d\u901a\u8fc7\u6307\u5b9a\u4e00\u4e2a\u5355\u5143\u7684\u72b6\u6001\u53d8\u5316\u6765\u7f16\u7801\uff0c\u4ee5\u54cd\u5e94\u5176\u90bb\u5c45\u5728\u5148\u524d\u65f6\u95f4\u6b65\u9aa4\u4e2d\u7684\u76f8\u5e94\u72b6\u6001\u53d8\u5316\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5e95\u5c42\u52a8\u529b\u5b66\u65b9\u7a0b\u53ef\u4ee5\u7528\u5178\u578b\u7684\u6613\u611f-\u611f\u67d3-\u6613\u611f<\/span>\uff08SIS\uff09<\/span>\u6a21\u578b\u6765\u5199\uff0c\u901a\u8fc7\u5c06\u91cd\u6784\u95ee\u9898\u6620\u5c04\u5230\u89e3\u51b3\u4e00\u4e2a\u51f8\u4f18\u5316\u95ee\u9898\uff0c\u5982\u538b\u7f29\u611f\u5e94[111]\u3002\u867d\u7136\u8fd9\u79cd\u65b9\u6cd5\u5728\u5176\u5de5\u4f5c\u5047\u8bbe\u4e0b\u662f\u5f3a\u5927\u7684\uff0c\u4f46\u5b83\u53ea\u9650\u4e8e\u6240\u8003\u8651\u7684\u52a8\u529b\u5b66\u7cfb\u7edf\u7c7b\u522b\u3002\u7136\u800c\uff0c\u5b83\u63d0\u4f9b\u4e86\u4e00\u4e2a\u6709\u5e0c\u671b\u7684\u7a0b\u5e8f\uff0c\u53ef\u4ee5\u9002\u7528\u4e8e\u5176\u4ed6\u53cd\u95ee\u9898\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5c06\u91cd\u6784\u95ee\u9898\u8f6c\u5316\u4e3a\u7a00\u758f\u4fe1\u53f7\u91cd\u6784\u95ee\u9898\u7684\u76f8\u540c\u6280\u5de7\u53ef\u4ee5\u5e94\u7528\u4e8e\u5176\u4ed6\u60c5\u51b5\uff0c\u5982\u8fdb\u5316\u6e38\u620f\u548c\u901a\u4fe1\u8fc7\u7a0b\uff0c\u5176\u4e2d\u53e6\u4e00\u79cd\u51f8\u4f18\u5316\u65b9\u6cd5\uff0c\u5373 LASSO\uff0c\u751a\u81f3\u53ef\u4ee5\u7528\u4e8e\u5b58\u5728\u566a\u58f0\u7684\u65f6\u95f4\u5e8f\u5217\u548c\u90e8\u5206\u7f3a\u5931\u7684\u8282\u70b9\u6570\u636e[112]\u3002<\/span><\/section>\n

<\/section>\n
\u53e6\u4e00\u79cd\u53ef\u80fd\u6027\u662f\u5229\u7528\u5145\u5206\u9a71\u52a8\u4fe1\u53f7\u7684\u4e0d\u53d8\u63aa\u65bd\u7684\u53cd\u5e94\u6765\u91cd\u6784\u7cfb\u7edf\u5355\u5143\u4e4b\u95f4\u7684\u7269\u7406\u76f8\u4e92\u4f5c\u7528\u3002\u5728\u6e29\u548c\u7684\u5047\u8bbe\u4e0b\uff0c\u53ef\u4ee5\u8bc1\u660e\u5e73\u5747\u9a71\u52a8\u4fe1\u53f7\u7684\u77e2\u91cf\u53ef\u4ee5\u4e0e\u54cd\u5e94\u5dee\u5f02\u548c\u57fa\u672c\u52a8\u529b\u5b66\u7684\u96c5\u53ef\u6bd4\u77e9\u9635<\/span>\uff08Jacobian matrix\uff09<\/span>\u76f4\u63a5\u76f8\u5173\u3002\u53d7\u63a7\u6270\u52a8\u5b9e\u9a8c\u7684\u6570\u91cf\u8d8a\u591a\uff0c\u91cd\u6784\u7684\u7cbe\u5ea6\u5c31\u8d8a\u9ad8\u3002\u7136\u800c\uff0c\u5f80\u5f80\u5b9e\u73b0\u8bb8\u591a\u8fd9\u6837\u7684\u5b9e\u9a8c\u662f\u4e0d\u73b0\u5b9e\u7684\uff1a\u4e3a\u6b64\uff0c\u4eba\u4eec\u53ef\u4ee5\u5229\u7528\u538b\u7f29\u611f\u77e5\u6765\u5bfb\u627e\u76f8\u5e94\u7684\u4f18\u5316\u95ee\u9898\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u5728\u91cd\u6784\u7ecf\u9a8c\u7f51\u7edc\u65b9\u9762\u53d6\u5f97\u663e\u8457\u7684\u51c6\u786e\u6027\uff0c\u5982\u679c\u8747\u7684\u663c\u591c\u949f\u7f51\u7edc[97]\u3002\u8fd9\u79cd\u6280\u672f\u5f88\u5f3a\u5927\uff0c\u4f46\u5176\u6027\u80fd\u53ef\u80fd\u5173\u952e\u53d6\u51b3\u4e8e\u53ef\u7528\u5b9e\u9a8c\u7684\u6570\u91cf\u3002<\/span><\/section>\n

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5. \u65b9\u6cd5\u7684\u9002\u7528\u6027<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n
 <\/span><\/section>\n
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\u5728\u4e0b\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u5f3a\u8c03\u5f53\u7f51\u7edc\u63cf\u8ff0\u7b26\u4ee5\u4e0d\u6070\u5f53\u7684\u65b9\u5f0f\u88ab\u4f7f\u7528\u65f6\u51fa\u73b0\u7684\u4e00\u4e9b\u5e38\u89c1\u95ee\u9898\u3002<\/span><\/section>\n

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<\/section>\n

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\u5176\u4e2d P(A\u2223b) \u662f SBM \u7684\u53ef\u80fd\u6027\uff0c\u8fd9\u662f\u4e00\u4e2a\u8003\u8651\u5230\u7f51\u7edc\u6a21\u5757\u5316\u7ed3\u6784\u7684\u7f51\u7edc\u7ed3\u6784\u751f\u6210\u6a21\u578b\u3002\u6b63\u5982\u6211\u4eec\u5728\u56fe3c\u4e2d\u770b\u5230\u7684\uff0c\u5f53\u5e94\u7528\u4e8e\u540c\u4e00\u4e2a\u7f51\u7edc\u65f6\uff0c\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u4ec5\u53ef\u4ee5\u5b8c\u7f8e\u5730\u8bc6\u522b\u51fa\u5b8c\u5168\u5b50\u56fe\uff0c\u800c\u4e14\u8fd8\u53ef\u4ee5\u6b63\u786e\u5730\u786e\u5b9a\u5176\u4f59\u7684\u8282\u70b9\u5c5e\u4e8e\u540c\u4e00\u4e2a\u5206\u533a\uff0c\u4e5f\u5c31\u662f\u8bf4\u5b83\u4eec\u90fd\u6709\u76f8\u540c\u7684\u6982\u7387\u8fde\u63a5\u5230\u7f51\u7edc\u7684\u5176\u4ed6\u90e8\u5206\u3002\u8fd9\u79cd\u65b9\u6cd5\u6548\u679c\u66f4\u597d\uff0c\u56e0\u4e3a\u5b83\u76f8\u5f53\u4e8e\u95ee\u4e86\u4e00\u4e2a\u66f4\u5408\u9002\u7684\u57fa\u672c\u95ee\u9898\uff1a\u7f51\u7edc\u6700\u53ef\u80fd\u88ab\u5206\u6210\u7684\u7ec4\u662f\u4ec0\u4e48\uff1f\u9664\u4e86\u901a\u8fc7\u516c\u5f0f\uff084\uff09\u4e4b\u5916\uff0c\u4e0d\u53ef\u80fd\u4ee5\u4efb\u4f55\u5176\u4ed6\u65b9\u5f0f\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\uff1b\u5c3d\u7ba1\u6211\u4eec\u53ef\u4ee5\u4ee5\u8bb8\u591a\u65b9\u5f0f\u9009\u62e9\u5176\u90e8\u5206[129]\u3002\u987a\u4fbf\u63d0\u4e00\u4e0b\uff0c\u7528\u8fd9\u79cd\u65b9\u6cd5\u6211\u4eec\u4e5f\u80fd\u6bd4\u901a\u8fc7\u6a21\u5757\u5316\u66f4\u660e\u786e\u5730\u62d2\u7edd\u5b8c\u5168\u968f\u673a\u7f51\u7edc\u7684\u96f6\u6a21\u578b\u3002\u539f\u56e0\u662f\u5b8c\u5168\u968f\u673a\u7684\u7f51\u7edc\u76f8\u5f53\u4e8e\u5177\u6709\u5355\u4e00\u7ec4\u7684 SBM \u7684\u4e00\u4e2a\u7279\u4f8b\uff0c\u5bf9\u4e8e\u5b83\u6211\u4eec\u80fd\u591f\u5199\u51fa\u4e00\u4e2a\u7cbe\u786e\u7684\u540e\u9a8c\u6982\u7387\u3002\u7136\u800c\uff0c\u5c3d\u7ba1\u8fd9\u79cd\u65b9\u6cd5\u5728\u6982\u5ff5\u4e0a\u3001\u7406\u8bba\u4e0a\u548c\u5b9e\u8df5\u4e0a\u90fd\u6709\u4f18\u52bf\uff0c\u4f46\u5b83\u8fd8\u6ca1\u6709\u8fbe\u5230\u67d0\u4e9b\u5e94\u7528\u9886\u57df\u3002<\/span><\/section>\n

<\/section>\n
\u901a\u8fc7\u95ee\u81ea\u5df1\u4e3a\u4ec0\u4e48\u8fd9\u4e9b\u65b9\u6cd5\u6ca1\u6709\u6e17\u900f\u5230\u7f51\u7edc\u79d1\u5b66\u7684\u5168\u90e8\u9886\u57df\uff0c\u6211\u4eec\u53ef\u4ee5\u627e\u51fa\u4e00\u4e9b\u53ef\u80fd\u6027\u3002\u4e00\u4e2a\u7279\u522b\u7684\u95ee\u9898\u662f\uff0c\u7814\u7a76\u4eba\u5458\u53d7\u5236\u4e8e\u5bfb\u627e\u4e0b\u4e00\u4e2a\u91cd\u5927\u7a81\u7834\u7684\u52a8\u673a\uff0c\u800c\u4e0d\u662f\u63a2\u7d22\u73b0\u6709\u65b9\u6cd5\u4e4b\u95f4\u7684\u7b49\u4ef7\u6027[130,131]\uff0c\u6216\u8005\u91cd\u65b0\u5ba1\u89c6\u5148\u524d\u7684\u5de5\u4f5c\u6216\u65e2\u5b9a\u7684\u4fe1\u5ff5<\/span>\uff08\u4f8b\u5982\uff0c\u8282\u70b9\u5c5e\u6027\u4e0d\u662f\u771f\u6b63\u7684\u793e\u533a[132]\uff0c\u7f51\u7edc\u6570\u636e\u662f\u4e0d\u786e\u5b9a\u7684[43]\uff0c\u9608\u503c\u5316\u76f8\u5173\u77e9\u9635\u662f\u5f92\u52b3\u7684[65]\uff09<\/span>\uff0c\u5e76\u53ef\u80fd\u91cd\u65b0\u53d1\u660e\u8f66\u8f6e[133]\u3002\u793e\u533a\u68c0\u6d4b\u63d0\u4f9b\u4e86\u4e00\u4e2a\u7279\u6b8a\u7684\u6848\u4f8b\uff0c\u56e0\u4e3a SBM \u6700\u65e9\u662f\u5728\u51e0\u5341\u5e74\u524d\u5f00\u53d1\u7684[134,135]<\/span>\uff08\u5c3d\u7ba1\u5176\u63a8\u65ad\u7684\u7a33\u5065\u548c\u6709\u6548\u7684\u65b9\u6cd5\u662f\u5728\u8fc7\u53bb\u5341\u5e74\u624d\u5f00\u53d1\u7684\uff09<\/span>\u3002\u81ea\u4ece\u5f15\u5165\u793e\u7fa4\u68c0\u6d4b\u95ee\u9898[136]\u4ee5\u6765\uff0c\u6211\u4eec\u770b\u5230\u4e86\u5927\u91cf\u7684\u65b9\u6cd5\u88ab\u5f00\u53d1\u51fa\u6765\uff0c\u9020\u6210\u4e86\u7406\u8bba\u4e0a\u7684\u4e0d\u4e00\u81f4\u3002\u4e00\u4e2a\u4e0d\u5e78\u7684\u7ed3\u679c\u662f\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u4e2d\u6709\u8bb8\u591a\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f SBM \u6846\u67b6\u539f\u5219\u6027\u8f83\u4f4e\u7684\u53d8\u79cd\u6216\u8fd1\u4f3c[130]\u3002\u8fd9\u79cd\u5bf9\u95ee\u9898\u7a7a\u95f4\u7684\u7279\u5b9a\u90e8\u5206\u7684\u8fc7\u5ea6\u63a2\u7d22\uff0c\u51e0\u4e4e\u80af\u5b9a\u662f\u4ee5\u5ffd\u89c6\u7f51\u7edc\u805a\u7c7b\u7684\u5176\u4ed6\u76f8\u5173\u95ee\u9898\u4e3a\u4ee3\u4ef7\u7684[126,137]\u3002<\/span><\/section>\n

<\/section>\n
\uff08II\uff09\u5bf9\u91cd\u6784\u4e0d\u786e\u5b9a\u6027\u7684\u8003\u8651\u3002<\/strong>\u8fd8\u6709\u4e00\u4e9b\u5b9e\u9645\u60c5\u51b5\uff0c\u4eba\u4eec\u5bf9\u6570\u636e\u63d0\u51fa\u4e86\u9519\u8bef\u7684\u95ee\u9898\u3002\u7531\u4e8e\u4efb\u4f55\u73b0\u5b9e\u4e16\u754c\u7684\u6d4b\u91cf\u90fd\u4f1a\u53d7\u5230\u6d4b\u91cf\u8bef\u5dee\u7684\u5f71\u54cd\uff0c\u6240\u4ee5\u5728\u4f30\u8ba1\u7f51\u7edc\u63cf\u8ff0\u7b26\u65f6\uff0c\u5e94\u8be5\u8003\u8651\u5230\u5b83\u4eec\u4ee5\u53ca\u5b83\u4eec\u7684\u4f20\u64ad\uff0c\u8fd9\u662f\u6807\u51c6\u7684\u505a\u6cd5\u3002\u8fd9\u5c06\u4f7f\u6211\u4eec\u80fd\u591f\u91cf\u5316\u6211\u4eec\u4f30\u8ba1\u7684\u4e0d\u786e\u5b9a\u6027\uff0c\u5e76\u5728\u4e0d\u540c\u7684\u6d4b\u91cf\u548c\u5b9e\u9a8c\u4e2d\u6bd4\u8f83\u7ed3\u679c\uff0c\u5c31\u50cf\u4efb\u4f55\u5b9a\u91cf\u5b66\u79d1\u4e00\u6837\u3002\u76f8\u53cd\uff0c\u5982\u679c\u7f3a\u4e4f\u8fd9\u6837\u4e00\u4e2a\u5408\u9002\u7684\u7a0b\u5e8f\uff0c\u5c31\u4e0d\u53ef\u907f\u514d\u5730\u5bfc\u81f4\u65e0\u6cd5\u5728\u4e0d\u540c\u7684\u5b9e\u9a8c\u4e2d\u8fdb\u884c\u6bd4\u8f83\u7684\u4f30\u8ba1\uff0c\u4ece\u800c\u5bfc\u81f4\u4e0d\u5bb9\u6613\u89e3\u51b3\u7684\u77db\u76fe\u7ed3\u679c\u3002<\/span><\/section>\n

<\/section>\n
\u8ba9\u6211\u4eec\u518d\u8003\u8651\u4e00\u4e0b\u8fd9\u6837\u7684\u60c5\u51b5\uff1a\u5e95\u5c42\u7f51\u7edc\u7ed3\u6784\u4e0d\u4e3a\u4eba\u77e5\uff0c\u4f46\u6709\u53ef\u80fd\u4ece\u8282\u70b9\u4e0a\u6d4b\u91cf\u4e00\u4e9b\u4fe1\u53f7<\/span>\uff08\u89c1\u56fe4\uff09<\/span>\u3002\u5f88\u591a\u65f6\u5019\uff0c\u76f8\u5173\u6216\u56e0\u679c\u5206\u6790\u88ab\u7528\u6765\u8868\u793a\u7cfb\u7edf\u5355\u5143\u4e4b\u95f4\u7684\u529f\u80fd\u5173\u7cfb\uff0c\u5e76\u4ece\u8fd9\u79cd\u8868\u793a\u4e2d\u8fde\u7eed\u8ba1\u7b97\u7f51\u7edc\u63cf\u8ff0\u7b26\u3002<\/span><\/section>\n

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

\u56fe4\uff1a\u5728\u4e0d\u786e\u5b9a\u6027\u4e0b\u6d4b\u91cf\u7f51\u7edc\u63cf\u8ff0\u7b26\u3002\u5728\u8bb8\u591a\u5b9e\u9645\u95ee\u9898\u4e2d\uff0c\u7f51\u7edc\u7684\u7ed3\u6784\u65e0\u6cd5\u76f4\u63a5\u89c2\u5bdf\uff0c\u800c\u4fe1\u53f7\uff08\u5982\u7269\u7406\u53d8\u91cf\u7684\u65f6\u95f4\u8fc7\u7a0b\uff09\u53ef\u4ee5\u4ece\u5176\u5355\u5143\u4e2d\u6d4b\u91cf\u3002\u5728\u5e94\u7528\u4e86\u7b2c\u4e8c\u8282\u4e2d\u63cf\u8ff0\u7684\u6709\u6548\u7684\u91cd\u6784\u65b9\u6cd5\u540e\uff0c\u7ed3\u679c\u53ef\u4ee5\u901a\u8fc7\u6bcf\u4e2a\u6210\u5bf9\u94fe\u63a5\u5b58\u5728\u7684\u8fb9\u9645\u6982\u7387\u4ee5\u4e00\u79cd\u65b9\u4fbf\u7684\u65b9\u5f0f\u8fdb\u884c\u603b\u7ed3\uff0c\u4ee3\u4ef7\u662f\u635f\u5931\u4e86\u5168\u90e8\u8054\u5408\u5206\u5e03\u4e2d\u7684\u4e00\u4e9b\u4fe1\u606f\u3002\u8bf7\u6ce8\u610f\uff0c\u8fd9\u4e9b\u6982\u7387\u7684\u96c6\u5408\u5e76\u4e0d\u4ee3\u8868\u4e00\u4e2a\u52a0\u6743\u6216\u6709\u5411\u7f51\u7edc\uff0c\u5728\u76f8\u5e94\u7684\u56fe\u4e0a\u8fdb\u884c\u4efb\u4f55\u6807\u51c6\u7684\u7f51\u7edc\u5206\u6790\u90fd\u662f\u9519\u8bef\u7684\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5355\u4e2a\u8282\u70b9\u6216\u6574\u4e2a\u7f51\u7edc\u5c42\u9762\u7684\u5355\u4e00\u6d4b\u91cf\u88ab\u6982\u7387\u5206\u5e03\u6240\u53d6\u4ee3\uff0c\u7f16\u7801\u6d4b\u91cf\u4e00\u4e2a\u7279\u5b9a\u503c\u7684\u53ef\u80fd\u6027\u3002\u4f8b\u5982\uff0c\u5728\u4e00\u4e2a\u5927\u5c0f\u4e3a N \u7684\u7f51\u7edc\u4e2d\uff0c\u4ee3\u66ff\u5355\u4e2a\u8282\u70b9 i \u7684\u5ea6\u6570 ki<\/sub><\/span> \u7684\u662f\u4f30\u8ba1\u8be5\u8282\u70b9\u5177\u6709\u5ea6\u6570k\u7684\u6982\u7387 P\uff08ki<\/sub><\/span> = k\uff09\uff0ck = 0,1,…,N\u3002\u540c\u6837\u5730\uff0c\u8282\u70b9 i \u7684\u8de8\u5ea6 ci<\/sub><\/span> \u88ab\u66ff\u6362\u4e3a\u8be5\u8282\u70b9\u5177\u6709\u8de8\u5ea6 c \u7684\u6982\u7387 P(ci<\/sub><\/span> = c)\uff0c\u8fd9\u53ef\u80fd\u5bf9\u5e94\u4e8e\u591a\u4e2a\u5c40\u90e8\u914d\u7f6e\u800c\u4e0d\u662f\u4e00\u4e2a\u7279\u5b9a\u7684\u914d\u7f6e\uff0c\u5982\u56fe\u4e2d\u53f3\u4fa7\u6240\u793a\u3002\u8fd9\u79cd\u6982\u7387\u5206\u5e03\u53ef\u4ee5\u5728\u7528\u4e8e\u5efa\u7acb\u6982\u7387\u7f51\u7edc\u6a21\u578b\u7684\u8d1d\u53f6\u65af\u63a8\u7406\u6846\u67b6\u5185\u5f97\u5230[106]\u3002<\/span><\/p>\n


<\/section>\n
\u5728\u5e94\u7528\u6709\u6548\u7684\u91cd\u6784\u65b9\u6cd5\u540e\uff0c\u5982\u7b2c\uff08II\uff09\u8282\u6240\u8ff0\uff0c\u4e5f\u6709\u53ef\u80fd\u4ee5\u4e00\u79cd\u65b9\u4fbf\u7684\u65b9\u5f0f\u603b\u7ed3\u8282\u70b9 i \u548c j \u4e4b\u95f4\u5b58\u5728\u8fb9\u7f18\u7684\u8fb9\u9645\u6982\u7387 pij<\/sub><\/span>\uff0c\u4ee5\u73b0\u6709\u7684\u6570\u636e\u4e3a\u6761\u4ef6\uff0c\u4ee5\u635f\u5931\u5b8c\u6574\u8054\u5408\u5206\u5e03\u4e2d\u7684\u4e00\u4e9b\u4fe1\u606f\u4e3a\u4ee3\u4ef7\u3002\u8fd9\u4e2a\u6b65\u9aa4\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u53ef\u80fd\u662f\u5fc5\u8981\u7684\uff0c\u4f8b\u5982\uff0c\u5f53\u4e00\u4e2a\u5408\u7406\u7684\u52a8\u529b\u5b66\u6a21\u578b\u8fd8\u4e0d\u6e05\u695a\u7684\u65f6\u5019\u3002<\/span><\/section>\n

<\/section>\n
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\u57fa\u4e8e\u6211\u4eec\u7684\u5206\u6790\uff0c\u6211\u4eec\u53ef\u4ee5\u4e3a\u7f51\u7edc\u79d1\u5b66\u7684\u4e0b\u4e00\u6b65\u53d1\u5c55\u53ca\u5176\u5bf9\u7279\u5b9a\u9886\u57df\u6311\u6218\u7684\u5e94\u7528\u786e\u5b9a\u4e00\u5957\u7b80\u6d01\u7684\u6700\u4f73\u5b9e\u8df5\u3002\u9996\u5148\uff0c\u6211\u4eec\u5fc5\u987b\u4e86\u89e3\u7f51\u7edc\u6570\u636e\u7684\u51fa\u5904\uff0c\u5e76\u901a\u8fc7\u751f\u6210\u6a21\u578b\uff0c\u660e\u786e\u5e0c\u671b\u4ece\u5176\u4e2d\u63d0\u53d6\u7684\u57fa\u672c\u62bd\u8c61\u3002\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u9009\u62e9\u7684\u62bd\u8c61\u4e0d\u5e94\u8be5\u4f9d\u8d56\u4e8e\u7a7a\u95f4\u548c\/\u6216\u65f6\u95f4\u7c92\u5ea6\u7684\u4efb\u610f\u9009\u62e9\uff0c\u6216\u8005\u6211\u4eec\u81f3\u5c11\u5e94\u8be5\u8bc1\u660e\u6240\u4ea7\u751f\u7684\u5206\u6790\u5bf9\u8fd9\u79cd\u9009\u62e9\u4e0d\u654f\u611f\u3002\u7b2c\u4e8c\uff0c\u6211\u4eec\u5fc5\u987b\u5728\u7406\u8bba\u4e0a\u548c\u5b9e\u8df5\u4e2d\u7eb3\u5165\u7f51\u7edc\u6d4b\u91cf\u4e2d\u7684\u9519\u8bef\u548c\u4e0d\u5b8c\u6574\u7684\u5b58\u5728\u548c\u5f71\u54cd\u3002\u7b2c\u4e09\uff0c\u5f53\u5f00\u53d1\u4e00\u4e2a\u65b0\u7684\u5206\u6790\u65b9\u6cd5\u65f6\uff0c\u6211\u4eec\u5e94\u8be5\u5728\u5408\u6210\u6570\u636e\u4e0a\u9a8c\u8bc1\u5b83\uff0c\u4ee5\u4fdd\u8bc1\u627e\u5230\u9884\u671f\u7684\u7ed3\u679c\u3002\u5982\u679c\u4e00\u79cd\u65b9\u6cd5\u7684\u6709\u6548\u6027\u4e0d\u80fd\u5728\u53d7\u63a7\u7684\u5408\u6210\u5b9e\u9a8c\u4e2d\u5f97\u5230\u8bc1\u660e\uff0c\u90a3\u4e48\u5f53\u5b83\u88ab\u5e94\u7528\u4e8e\u7ecf\u9a8c\u6570\u636e\u65f6\u5f97\u5230\u7684\u7ed3\u679c\u5c31\u6ca1\u6709\u4ec0\u4e48\u4ef7\u503c\u3002<\/span><\/section>\n

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\u5728\u7279\u5b9a\u7ecf\u9a8c\u79d1\u5b66\u9886\u57df\u7684\u7814\u7a76\u4eba\u5458\u773c\u91cc\uff0c\u6211\u4eec\u6240\u8ba8\u8bba\u7684\u5927\u90e8\u5206\u5185\u5bb9\u53ef\u80fd\u770b\u8d77\u6765\u662f\u6807\u51c6\u548c\u65e2\u5b9a\u7684\u51c6\u5219\u3002\u6211\u4eec\u5728\u8fd9\u91cc\u5f3a\u8c03\u7684\u662f\uff0c\u5982\u679c\u4e0d\u66f4\u666e\u904d\u5730\u91c7\u7528\u4e25\u683c\u7684\u65b9\u6cd5\u8bba\uff0c\u5c31\u4f1a\u51fa\u73b0\u4e00\u4e9b\u5fae\u5999\u7684\u95ee\u9898\u3002\u7f51\u7edc\u79d1\u5b66\u754c\u7684\u7279\u70b9\u662f\u5176\u6210\u5458\u7684\u5f02\u8d28\u6027\u80cc\u666f\uff0c\u8fd9\u662f\u6211\u4eec\u793e\u533a\u7684\u4f18\u52bf\u4e4b\u4e00\u3002\u7136\u800c\uff0c\u8fd9\u79cd\u5f02\u8d28\u6027\u4e5f\u610f\u5473\u7740\uff0c\u4e0a\u8ff0\u7684\u8bb8\u591a\u89c2\u70b9\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u6574\u4f53\uff0c\u5e76\u6ca1\u6709\u5f97\u5230\u666e\u904d\u7684\u8ba4\u53ef\uff0c\u56e0\u6b64\u9700\u8981\u5f3a\u8c03\u3002\u4f8b\u5982\uff0c\u5728\u7279\u5b9a\u5b66\u79d1\u8303\u56f4\u5185\u5bb9\u6613\u8bc6\u522b\u7684\u65b9\u6cd5\u5b66\u7f3a\u9677\uff0c\u5373\u4f7f\u5e94\u7528\u4e8e\u76f8\u540c\u7684\u6570\u636e\uff0c\u5728\u66f4\u5e7f\u6cdb\u7684\u7f51\u7edc\u79d1\u5b66\u8303\u56f4\u5185\uff0c\u4e5f\u4e0d\u53ef\u907f\u514d\u5730\u4f1a\u5bfc\u81f4\u6709\u4e89\u8bae\u7684\u7ed3\u679c\u3002\u56e0\u6b64\uff0c\u6709\u5fc5\u8981\u8d85\u8d8a\u4e2a\u522b\u5b66\u79d1\u7684\u7279\u5b9a\u8bed\u8a00\u548c\u5b9e\u8df5\uff0c\u79ef\u6781\u5730\u8fdb\u884c\u4ea4\u53c9\u6388\u7c89\uff0c\u4ee5\u4fbf\u5728\u6211\u4eec\u7684\u591a\u5b66\u79d1\u9886\u57df\u83b7\u5f97\u4e00\u4e2a\u5171\u540c\u7684\u6700\u4f73\u5b9e\u8df5\u6807\u51c6\u3002<\/span><\/section>\n

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\u53ea\u6709\u5728\u8d1f\u8d23\u4efb\u5730\u4f7f\u7528\u5e76\u5177\u6709\u9002\u5f53\u6c34\u5e73\u7684\u65b9\u6cd5\u8bba\u4e25\u8c28\u6027\u7684\u60c5\u51b5\u4e0b\uff0c\u7f51\u7edc\u79d1\u5b66\u7684\u5de5\u5177\u624d\u80fd\u8ba9\u6211\u4eec\u5bf9\u590d\u6742\u7cfb\u7edf\u7684\u7ed3\u6784\u3001\u529f\u80fd\u548c\u52a8\u529b\u5b66\u6709\u72ec\u7279\u7684\u6d1e\u5bdf\u529b\u3002<\/span><\/span><\/section>\n

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    \n
  1. \n
    Newman, M. E. J. The structure and function of complex networks. SIAM Rev.45, 167\u2013256 (2003).<\/section>\n<\/li>\n
  2. \n
    Boccaletti, S., Latora, V., Moreno, Y., Chavez, M. & Hwang, D. U. Complex networks: Structure and dynamics. Phys. Reports.424, 175\u2013308 (2006).<\/section>\n<\/li>\n
  3. \n
    Guimer\u00e1, R. & Nunes Amaral, L. A. Functional cartography of complex metabolic networks. Nature433, 895\u2013900 (2005).<\/section>\n<\/li>\n
  4. \n
    Yu, H. et al. High-quality binary protein interaction map of the yeast interactome network. Science (New York, N.Y.)322, 104\u2013110 (2008).<\/section>\n<\/li>\n
  5. \n
    Costanzo, M. et al. The genetic landscape of a cell. Science327, 425\u2013431 (2010).<\/section>\n<\/li>\n
  6. \n
    Bassett, D. S. et al. Dynamic reconfiguration of human brain networks during learning. Proc. National Acad. Sci.108, 7641\u20137646 (2011).<\/section>\n<\/li>\n
  7. \n
    Bullmore, E. & Sporns, O. The economy of brain network organization. Nat. Rev. Neurosci.13, 336\u2013349 (2012).<\/section>\n<\/li>\n
  8. \n
    de  Vico Fallani, F., Richiardi, J., Chavez, M. & Achard, S. Graph  analysis of functional brain networks: practical issues in translational  neuroscience. Philosophical Transactions Royal Society B: Biological Sci.369, 20130521 (2014).<\/section>\n<\/li>\n
  9. \n
    Bascompte, J., Jordano, P. & Olesen, J. M. Asymmetric coevolutionary networks facilitate biodiversity maintenance. Science312, 431\u2013433 (2006).<\/section>\n<\/li>\n
  10. \n
    Ings, T. C. et al. Ecological networks\u2013beyond food webs. J. Animal Ecol.78, 253\u2013269 (2009).<\/section>\n<\/li>\n
  11. \n
    Pilosof, S., Porter, M. A., Pascual, M. & K\u00e9fi, S. The multilayer nature of ecological networks. Nat. Ecol. Evolution.1, 1\u20139 (2017).<\/section>\n<\/li>\n
  12. \n
    Rosato, V. et al. Modelling interdependent infrastructures using interacting dynamical models. Int. J. Critical Infra.4, 63\u201379 (2008).<\/section>\n<\/li>\n
  13. \n
    Buldyrev,  S. V., Parshani, R., Paul, G., Stanley, H. E. & Havlin, S.  Catastrophic cade of failures in interdependent networks. Nature464, 1025\u20131028 (2010).<\/section>\n<\/li>\n
  14. \n
    Pastor-Satorras, R., V\u00e1zquez, A. & Vespignani, A. Dynamical and correlation properties of the internet. Phys. Rev. lett.87, 258701 (2001).<\/section>\n<\/li>\n
  15. \n
    Mahadevan, P. et al. The internet as-level topology: three data sources and one definitive metric. ACM SIGCOMM Computer Communication Rev.36, 17\u201326 (2006).<\/section>\n<\/li>\n
  16. \n
    Watts, D. J. A simple model of global cades on random networks. Proc. National Academy Sci.99, 5766\u20135771 (2002).<\/section>\n<\/li>\n
  17. \n
    Kossinets, G. & Watts, D. J. Empirical analysis of an evolving social network. Science311, 88\u201390 (2006).<\/section>\n<\/li>\n
  18. \n
    Fowler, J. H. & Christakis, N. A. Cooperative behavior cades in human social networks. Proc. National Acad. Sci.107, 5334\u20135338 (2010).<\/section>\n<\/li>\n
  19. \n
    Stella,  M., Ferrara, E. & De Domenico, M. Bots increase exposure to  negative and inflammatory content in online social systems. Proc. National Acad. Sci.115, 12435\u201312440 (2018).<\/section>\n<\/li>\n
  20. \n
    Silk, M. J., Finn, K. R., Porter, M. A. & Pinter-Wollman, N. Can multilayer networks advance animal behavior research? Trends Ecol. Evolution.33, 376\u2013378 (2018).<\/section>\n<\/li>\n
  21. \n
    Cai, W., Snyder, J., Hastings, A. & D\u2019Souza, R. M. Mutualistic networks emerging from adaptive niche-based interactions. Nat. Commun.11, 1\u201310 (2020).<\/section>\n<\/li>\n
  22. \n
    Christakis, N. A. & Fowler, J. H. The spread of obesity in a large social network over 32 years. New England J. Medicine.357, 370\u2013379 (2007).<\/section>\n<\/li>\n
  23. \n
    Gallotti,  R., Valle, F., taldo, N., Sacco, P. & De Domenico, M. Assessing  the risks of ?infodemics? in response to covid-19 epidemics. Nat. Human Behaviour.4, 1285\u20131293 (2020).<\/section>\n<\/li>\n
  24. \n
    Montoya, J. M., Pimm, S. L. & Sol\u00e9, R. V. Ecological networks and their fragility. Nature442, 259\u2013264 (2006).<\/section>\n<\/li>\n
  25. \n
    Bastolla, U. et al. The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature458, 1018\u20131020 (2009).<\/section>\n<\/li>\n
  26. \n
    Pocock, M. J., Evans, D. M. & Memmott, J. The robustness and restoration of a network of ecological networks. Science335, 973\u2013977 (2012).<\/section>\n<\/li>\n
  27. \n
    Goh, K. I. et al. The human disease network. Proc. National Acad. Sci.104, 8685 (2007).<\/section>\n<\/li>\n
  28. \n
    Vidal, M., Cusick, M. E. & Barab\u00e1si, A.-L. Interactome networks and human disease. Cell144, 986\u2013998 (2011).<\/section>\n<\/li>\n
  29. \n
    Halu, A., De Domenico, M., Arenas, A. & Sharma, A. The multiplex network of human diseases. NPJ Systems Biol. Applications.5, 1\u201312 (2019).<\/section>\n<\/li>\n
  30. \n
    Keeling, M. J. & Eames, K. T. Networks and epidemic models. J. Royal Society Interf.2, 295\u2013307 (2005).<\/section>\n<\/li>\n
  31. \n
    Colizza,  V., Barrat, A., Barth\u00e9lemy, M. & Vespignani, A. The role of the  airline transportation network in the prediction and predictability of  global epidemics. Proc. National Acad. Sci.103, 2015\u20132020 (2006).<\/section>\n<\/li>\n
  32. \n
    Balcan, D. et al. Multiscale mobility networks and the spatial spreading of infectious diseases. Proc. National Acad. Sci.106, 21484\u201321489 (2009).<\/section>\n<\/li>\n
  33. \n
    G\u00f3mez-Gardenes,  J., Soriano-Panos, D. & Arenas, A. Critical regimes driven by  recurrent mobility patterns of reaction\u2013diffusion processes in networks.  Nat. Phys.14, 391\u2013395 (2018).<\/section>\n<\/li>\n
  34. \n
    Zhang, J. et al. Changes in contact patterns shape the dynamics of the covid-19 outbreak in china. Science368, 1481\u20131486 (2020).<\/section>\n<\/li>\n
  35. \n
    Arenas,  A. et al. Modeling the spatiotemporal epidemic spreading of covid-19  and the impact of mobility and social distancing interventions. Phys. Rev. X.10, 041055 (2020).<\/section>\n<\/li>\n
  36. \n
    Butts, C. T. Network inference, error, and informant (in)accuracy: a Bayesian approach. Social Networks.25, 103\u2013140 (2003).<\/section>\n<\/li>\n
  37. \n
    Young, J.-G., Valdovinos, F. S. & Newman, M. E. J. Reconstruction of plant-pollinator networks from observational data. Nat. Commun.12, 3911 (2021).<\/section>\n<\/li>\n
  38. \n
    Zachary, W. W. An Information Flow Model for Conflict and Fission in Small Groups. J. Anthropological Res.33, 452\u2013473 (1977).<\/section>\n<\/li>\n
  39. \n
    Morstatter,  F., Pfeffer, J., Liu, H. & Carley, K.Is the sample good enough?  comparing data from Twitter\u2019s streaming api with Twitter\u2019s firehose. In Proc. of the International AAAI Conference on Web and Social Media, vol. 7 (2013).<\/section>\n<\/li>\n
  40. \n
    Mislove, A., Lehmann, S., Ahn, Y.-Y., Onnela, J.-P. & Rosenquist, J.Understanding the demographics of Twitter users. In Proc. of the International AAAI Conference on Web and Social Media, vol. 5 (2011).<\/section>\n<\/li>\n
  41. \n
    Moody, J. Peer influence groups: identifying dense clusters in large networks. Social Networks.23, 261\u2013283 (2001).<\/section>\n<\/li>\n
  42. \n
    Adamic, L. A. & Glance, N.The political blogosphere and the 2004 U.S. election: divided they blog. In Proceedings of the 3rd international workshop on Link discovery, LinkKDD \u201905, 36-43 (ACM, New York, NY, USA, 2005).<\/section>\n<\/li>\n
  43. \n
    Goldberg, D. S. & Roth, F. P. Assessing experimentally derived interactions in a small world. Proc. National Acad. Sci.100, 4372\u20134376 (2003).<\/section>\n<\/li>\n
  44. \n
    L\u00fc, L. & Zhou, T. Link prediction in complex networks: A survey. Physica A: Statistical Mechanics Applications.390, 1150\u20131170 (2011).<\/section>\n<\/li>\n
  45. \n
    Watts, D. J. & Strogatz, S. H. Collective dynamics of \u2019small-world\u2019 networks. Nature393, 409\u201310 (1998).<\/section>\n<\/li>\n
  46. \n
    Taskar, B., Wong, M.-F., Abbeel, P. & Koller, D. Link prediction in relational data. Adv. Neural Inform. Proc. Sys.16, 659\u2013666 (2003).<\/section>\n<\/li>\n
  47. \n
    Popescul,  A. & Ungar, L. H.Statistical relational learning for link  prediction. In IJCAI workshop on learning statistical models from  relational data, vol. 2003 (Citeseer, 2003).<\/section>\n<\/li>\n
  48. \n
    Guimer\u00e1, R. & Sales-Pardo, M. Missing and spurious interactions and the reconstruction of complex networks. Proc. National Acad. Sci.106, 22073 \u201322078 (2009).<\/section>\n<\/li>\n
  49. \n
    Clauset, A., Moore, C. & Newman, M. E. J. Hierarchical structure and the prediction of missing links in networks. Nature453, 98\u2013101 (2008).<\/section>\n<\/li>\n
  50. \n
    Airoldi, E. M., Blei, D. M., Fienberg, S. E. & Xing, E. P. Mixed Membership Stochastic Blockmodels. J. Mach. Learn. Res.9, 1981\u20132014 (2008).<\/section>\n<\/li>\n
  51. \n
    Liben-Nowell, D. & Kleinberg, J. The link-prediction problem for social networks. J. American Society Inform. Sci. Technol.58, 1019\u20131031 (2007).<\/section>\n<\/li>\n
  52. \n
    Newman, M. E. J. Network structure from rich but noisy data. Nat. Phys.14, 542\u2013545 (2018).<\/section>\n<\/li>\n
  53. \n
    Peixoto, T. P. Reconstructing Networks with Unknown and Heterogeneous Errors. Phys. Rev. X.8, 041011 (2018).<\/section>\n<\/li>\n
  54. \n
    Young,  J.-G., Cantwell, G. T. & Newman, M. E. J.Robust Bayesian inference  of network structure from unreliable data. arXiv:2008.03334 [physics,  stat] (2020).<\/section>\n<\/li>\n
  55. \n
    Newcombe, H. B., Kennedy, J. M., Axford, S. & James, A. P. Automatic linkage of vital records. Science130, 954\u2013959 (1959).<\/section>\n<\/li>\n
  56. \n
    Fellegi, I. P. & Sunter, A. B. A theory for record linkage. J. American Statistical Association.64, 1183\u20131210 (1969).<\/section>\n<\/li>\n
  57. \n
    Pasula, H., Marthi, B., Milch, B., Russell, S. J. & Shpitser, I.Identity uncertainty and citation matching. In Advances in neural information processing systems15, 1425\u20131432 (2003).<\/section>\n<\/li>\n
  58. \n
    McCallum, A. & Wellner, B. Conditional models of identity uncertainty with application to noun coreference. Adv. Neural Inform. Process. sys.17, 905\u2013912 (2004).<\/section>\n<\/li>\n
  59. \n
    Dong, X., Halevy, A. & Madhavan, J.Reference reconciliation in complex information spaces. In Proc.of the 2005 ACM SIGMOD international conference on Management of data, 85\u201396 (2005).<\/section>\n<\/li>\n
  60. \n
    Butts, C. T.Revisiting the Foundations of Network Analysis. Science. https:\/\/www.science.org\/doi\/abs\/10.1126\/science.1171022. (2009). American Association for the Advancement of Science.<\/section>\n<\/li>\n
  61. \n
    Whitney, H. Congruent graphs and the connectivity of graphs. American J. ematics.54, 150\u2013168 (1932).<\/section>\n<\/li>\n
  62. \n
    Harary, F. & Norman, R. Z. Some properties of line digraphs. Rendiconti del Circolo Matematico di Palermo9, 161\u2013168 (1960).<\/section>\n<\/li>\n
  63. \n
    Pearl,  J. Causality: Models, Reasoning and Inference (Cambridge University  Press, Cambridge, U.K.; New York, 2009), 2nd edition edn.<\/section>\n<\/li>\n
  64. \n
    Ulanowicz,  R. E. & DeAngelis, D. L.Network analysis of trophic dynamics in  south florida ecosystems. US Geological Survey Program on the South  Florida Ecosystem 114 (2005). http:\/\/sofia.usgs.gov\/projects\/atlss\/atlssabsfrsf.html.<\/section>\n<\/li>\n
  65. \n
    Dempster, A. P. Covariance selection. Biometrics157-175 (1972).<\/section>\n<\/li>\n
  66. \n
    Friedman, J., Hastie, T. & Tibshirani, R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics9, 432\u2013441 (2008).<\/section>\n<\/li>\n
  67. \n
    Nguyen, H. C., Zecchina, R. & Berg, J. Inverse statistical problems: from the inverse Ising problem to data science. Adv. Phys.66, 197\u2013261 (2017).<\/section>\n<\/li>\n
  68. \n
    Peixoto, T. P. Network Reconstruction and Community Detection from Dynamics. Phys. Rev. Lett.123, 128301 (2019).<\/section>\n<\/li>\n
  69. \n
    Rosenblum, M. et al. Reconstructing networks of pulse-coupled oscillators from spike trains. Phys. Rev. E.96, 012209 (2017).<\/section>\n<\/li>\n
  70. \n
    Guimer\u00e1, R. et al. A Bayesian machine scientist to aid in the solution of challenging scientific problems. Sci. Adv.6, eaav6971 (2020).<\/section>\n<\/li>\n
  71. \n
    Eagle, N. & (Sandy) Pentland, A. Reality Mining: Sensing Complex Social Systems. Personal Ubiquitous Comput. 10, 255\u2013268 (2006).<\/section>\n<\/li>\n
  72. \n
    Cattuto, C. et al. Dynamics of Person-to-Person Interactions from Distributed RFID Sensor Networks. PLOS ONE.5, e11596 (2010).<\/section>\n<\/li>\n
  73. \n
    Stopczynski, A. et al. Measuring Large-Scale Social Networks with High Resolution. PLOS ONE.9, e95978 (2014). Publisher: Public Library of Science.<\/section>\n<\/li>\n
  74. \n
    Holme, P. & Saram\u00e4ki, J. Temporal networks. Phys. Reports.519, 97\u2013125 (2012).<\/section>\n<\/li>\n
  75. \n
    Gemmetto,  V., Barrat, A. & Cattuto, C. Mitigation of infectious disease at  school: targeted class closure vs school closure. BMC Infect. Dis.14, 695 (2014).<\/section>\n<\/li>\n
  76. \n
    Voirin,  N. et al. Combining High-Resolution Contact Data with Virological Data  to Investigate Influenza Transmission in a Tertiary Care Hospital. Infect. Control Hospital Epidemiol.36, 254\u2013260 (2015).<\/section>\n<\/li>\n
  77. \n
    Fournet,  J. & Barrat, A. Epidemic risk from friendship network data: an  equivalence with a non-uniform sampling of contact networks. Sci. Reports.6, 24593 (2016).<\/section>\n<\/li>\n
  78. \n
    Fournet, J. & Barrat, A. Estimating the epidemic risk using non-uniformly sampled contact data. Sci. Reports.7, 9975 (2017).<\/section>\n<\/li>\n
  79. \n
    Sapienza,  A., Barrat, A., Cattuto, C. & Gauvin, L. Estimating the outcome of  spreading processes on networks with incomplete information: A  dimensionality reduction approach. Phys. Rev. E.98, 012317 (2018).<\/section>\n<\/li>\n
  80. \n
    Ciaperoni, M. et al. Relevance of temporal cores for epidemic spread in temporal networks. Sci. Reports.10, 12529 (2020).<\/section>\n<\/li>\n
  81. \n
    Cencetti, G. et al. Digital proximity tracing on empirical contact networks for pandemic control. Nat. Commun.12, 1655 (2021).<\/section>\n<\/li>\n
  82. \n
    Barrat,  A., Cattuto, C., Kivel\u00e4, M., Lehmann, S. & Saram\u00e4ki, J. Effect of  manual and digital contact tracing on COVID-19 outbreaks: a study on  empirical contact data. J. Royal Society Interface.18, 20201000 (2021).<\/section>\n<\/li>\n
  83. \n
    Colosi, E. et al. Screening and vaccination against COVID-19 to minimise school closure: a modelling study. Lancet Infect. Dis. 22,977\u2013989 (2022).<\/section>\n<\/li>\n
  84. \n
    Leith,  D. J. & Farrell, S. Coronavirus Contact Tracing: Evaluating The  Potential Of Using Bluetooth Received Signal Strength For Proximity  Detection (2020). Number: arXiv:2006.06822 arXiv:2006.06822 [cs, eess].<\/section>\n<\/li>\n
  85. \n
    Gehlke,  C. E. & Biehl, K. Certain effects of grouping upon the size of the  correlation coefficient in census tract material. J. American Statistical Association.29, 169\u2013170 (1934).<\/section>\n<\/li>\n
  86. \n
    Gallotti, R., Bazzani, A., Degli Esposti, M. & Rambaldi, S. Entropic measures of individual mobility patterns. J. Statistical Mechanics: Theory Experiment.2013, P10022 (2013).<\/section>\n<\/li>\n
  87. \n
    Gallotti, R., Louf, R., Luck, J.-M. & Barthelemy, M. Tracking random walks. J. Royal Society Interface.15, 20170776 (2018).<\/section>\n<\/li>\n
  88. \n
    Fornito,  A., Zalesky, A. & Bullmore, E. Fundamentals of Brain Network  Analysis (Academic Press, Amsterdam; Boston, 2016), reprint edition edn.<\/section>\n<\/li>\n
  89. \n
    Korhonen, O., Zanin, M. & Papo, D. Principles and open questions in functional brain network reconstruction. Human Brain Mapping.42, 3680\u20133711 (2021).<\/section>\n<\/li>\n
  90. \n
    Zanin,  M., Belkoura, S., Gomez, J., Alfaro, C. & Cano, J. Topological  structures are consistently overestimated in functional complex  networks. Sci. Reports.8, 1\u20139 (2018).<\/section>\n<\/li>\n
  91. \n
    Papo, D., Zanin, M., Mart\u00ednez, J. H. & Buld\u00fa, J. M. Beware of the small-world neuroscientist! Front. Human Neurosci.10, 96 (2016).<\/section>\n<\/li>\n
  92. \n
    Arslan, S. et al. Human brain mapping: A systematic comparison of parcellation methods for the human cerebral cortex. NeuroImage170, 5\u201330 (2018).<\/section>\n<\/li>\n
  93. \n
    Hoffmann, T., Peel, L., Lambiotte, R. & Jones, N. S. Community detection in networks without observing edges. Sci. Adv.6, eaav1478 (2020).<\/section>\n<\/li>\n
  94. \n
    Timme, M. Revealing Network Connectivity from Response Dynamics. Phys. Rev. Lett.98, 224101 (2007).<\/section>\n<\/li>\n
  95. \n
    Shandilya, S. G. & Timme, M. Inferring network topology from complex dynamics. New J. Phys.13, 013004 (2011).<\/section>\n<\/li>\n
  96. \n
    Timme, M. & adiego, J. Revealing networks from dynamics: an introduction. J. Physics A: ematical Theoretical.47, 343001 (2014).<\/section>\n<\/li>\n
  97. \n
    Nitzan, M., adiego, J. & Timme, M. Revealing physical interaction networks from statistics of collective dynamics. Sci. Adv.3, e1600396 (2017).<\/section>\n<\/li>\n
  98. \n
    adiego, J., Maoutsa, D. & Timme, M. Inferring Network Connectivity from Event Timing Patterns. Phys. Rev. Lett.121, 054101 (2018).<\/section>\n<\/li>\n
  99. \n
    adiego,  J., Nitzan, M., Hallerberg, S. & Timme, M. Model-free inference of  direct network interactions from nonlinear collective dynamics. Nat. Commun.8, 2192 (2017).<\/section>\n<\/li>\n
  100. \n
    Runge, J. et al. Identifying causal gateways and mediators in complex spatio-temporal systems. Nat. Commun.6, 8502 (2015).<\/section>\n<\/li>\n
  101. \n
    Tumminello,  M., Micciche, S., Lillo, F., Piilo, J. & Mantegna, R. N.  Statistically validated networks in bipartite complex systems. PloS one6, e17994 (2011).<\/section>\n<\/li>\n
  102. \n
    Boers, N. et al. Complex networks reveal global pattern of extreme-rainfall teleconnections. Nature566, 373\u2013377 (2019).<\/section>\n<\/li>\n
  103. \n
    Runge,  J., Nowack, P., Kretschmer, M., Flaxman, S. & Sejdinovic, D.  Detecting and quantifying causal associations in large nonlinear time  series datasets. Sci. Adv.5, eaau4996 (2019).<\/section>\n<\/li>\n
  104. \n
    Harnack, D., Laminski, E., Sch\u00fcnemann, M. & Pawelzik, K. R. Topological Causality in Dynamical Systems. Phys. Rev. Lett. 119, 098301(2017).<\/section>\n<\/li>\n
  105. \n
    Ye, H. et al. Equation-free mechanistic ecosystem foreting using empirical dynamic modeling. Proc. National Acad. Sci. United States of America112, E1569\u201376 (2015).<\/section>\n<\/li>\n
  106. \n
    Raimondo, S. & De Domenico, M. Measuring topological descriptors of complex networks under uncertainty. Phys. Rev. E.103, 022311 (2021).<\/section>\n<\/li>\n
  107. \n
    Stavroglou, S. K., Pantelous, A. A., Stanley, H. E. & Zuev, K. M. Unveiling causal interactions in complex systems. Proc. Natl. Acad. Sci.117, 7599\u20137605. http:\/\/www.pnas.org\/lookup\/doi\/10.1073\/pnas.1918269117 (2020).<\/section>\n<\/li>\n
  108. \n
    Wang, S. et al. Inferring dynamic topology for decoding spatiotemporal structures in complex heterogeneous networks. Proc. National Acad. Sci. United States of America115, 9300\u20139305 (2018).<\/section>\n<\/li>\n
  109. \n
    Barzel, B. & Barab\u00e1si, A.-L. Universality in network dynamics. Nature Physics advance online publication http:\/\/www.nature.com\/nphys\/journal\/vaop\/ncurrent\/full\/nphys2741.html (2013).<\/section>\n<\/li>\n
  110. \n
    Barzel, B., Liu, Y.-Y. & Barab\u00e1si, A.-L. Constructing minimal models for complex system dynamics. Nat. Commun.6, 1\u20138 (2015).<\/section>\n<\/li>\n
  111. \n
    Shen,  Z., Wang, W.-X., Fan, Y., Di, Z. & Lai, Y.-C. Reconstructing  propagation networks with natural diversity and identifying hidden  sources. Nat. Commun.5, 4323 (2014).<\/section>\n<\/li>\n
  112. \n
    Han, X., Shen, Z., Wang, W.-X. & Di, Z. Robust reconstruction of complex networks from sparse data. Phys. Rev. lett.114, 028701 (2015).<\/section>\n<\/li>\n
  113. \n
    Newman, M. E. J. & Girvan, M. Finding and evaluating community structure in networks. Phys. Revi E.69, 026113 (2004).<\/section>\n<\/li>\n
  114. \n
    Zhou, S. & Mondrag\u00f3n, R. J. The rich-club phenomenon in the internet topology. IEEE Commun. Lett.8, 180\u2013182 (2004).<\/section>\n<\/li>\n
  115. \n
    Guimer\u00e1, R., Sales-Pardo, M. & Amaral, L. A. N. Modularity from fluctuations in random graphs and complex networks. Phys. Rev. E.70, 025101 (2004).<\/section>\n<\/li>\n
  116. \n
    Bianconi, G., Pin, P. & Marsili, M. Assessing the relevance of node features for network structure. Proc. National Acad. Sci.106, 11433\u201311438 (2009).<\/section>\n<\/li>\n
  117. \n
    Peel, L., Larremore, D. B. & Clauset, A. The ground truth about metadata and community detection in networks. Sci. Adv.3, e1602548 (2017).<\/section>\n<\/li>\n
  118. \n
    Ehrhardt, B. & Wolfe, P. J. Network modularity in the presence of covariates. Siam Rev.61, 261\u2013276 (2019).<\/section>\n<\/li>\n
  119. \n
    Cinelli, M., Peel, L., Iovanella, A. & Delvenne, J.-C. Network constraints on the mixing patterns of binary node metadata. Phys. Rev. E.102, 062310 (2020).<\/section>\n<\/li>\n
  120. \n
    Fortunato, S. Community detection in graphs. Phys. Reports.486, 75\u2013174 (2010).<\/section>\n<\/li>\n
  121. \n
    Fortunato, S. & Barth\u00e9lemy, M. Resolution limit in community detection. Proc. National Acad. Sci.104, 36\u201341 (2007).<\/section>\n<\/li>\n
  122. \n
    Good, B. H., de Montjoye, Y.-A. & Clauset, A. Performance of modularity maximization in practical contexts. Phys. Rev. E.81, 046106 (2010).<\/section>\n<\/li>\n
  123. \n
    Ghasemian, A., Hosseinmardi, H. & Clauset, A. Evaluating Overfit and Underfit in Models of Network Community Structure. IEEE Transactions on Knowledge and Data Engineering1-1 (2019).<\/section>\n<\/li>\n
  124. \n
    McDiarmid, C. & Skerman, F. Modularity in random regular graphs and lattices. Electronic Notes in Discrete ematics.43, 431\u2013437 (2013).<\/section>\n<\/li>\n
  125. \n
    Reichardt, J. & Bornholdt, S. When are networks truly modular? Physica D: Nonlinear Phenomena.224, 20\u201326 (2006).<\/section>\n<\/li>\n
  126. \n
    Peixoto,  T. P. Descriptive vs. inferential community detection: pitfalls, myths  and half-truths. arXiv:2112.00183 [physics, stat] (2022). ArXiv:  2112.00183.<\/section>\n<\/li>\n
  127. \n
    Karrer, B. & Newman, M. E. J. Stochastic blockmodels and community structure in networks. Phys. Rev. E.83, 016107 (2011).<\/section>\n<\/li>\n
  128. \n
    Decelle,  A., Krzakala, F., Moore, C. & Zdeborov\u00e1, L. Asymptotic analysis of  the stochastic block model for modular networks and its algorithmic  applications. Phys. Rev. E.84, 066106 (2011).<\/section>\n<\/li>\n
  129. \n
    Peixoto,  T. P. Bayesian Stochastic Blockmodeling. In Advances in Network  Clustering and Blockmodeling, 289\u2013332 (John Wiley & Sons, Ltd,  2019).<\/section>\n<\/li>\n
  130. \n
    Young, J.-G., St-Onge, G., Desrosiers, P. & Dub\u00e9, L. J. Universality of the stochastic block model. Phys. Rev. E.98, 032309 (2018).<\/section>\n<\/li>\n
  131. \n
    Newman, M. E. J. Equivalence between modularity optimization and maximum likelihood methods for community detection. Phys.Rev. E.94, 052315 (2016).<\/section>\n<\/li>\n
  132. \n
    White,  H. C., Boorman, S. A. & Breiger, R. L. Social structure from  multiple networks. i. blockmodels of roles and positions. American J. Sociology.81, 730\u2013780 (1976).<\/section>\n<\/li>\n
  133. \n
    Price, Dd. S. A general theory of bibliometric and other cumulative advantage processes. J. American Society Inform. Sci.27, 292\u2013306 (1976).<\/section>\n<\/li>\n
  134. \n
    Holland, P. W., Laskey, K. B. & Leinhardt, S. Stochastic blockmodels: First steps. Social Networks.5, 109\u2013137 (1983).<\/section>\n<\/li>\n
  135. \n
    Nowicki, K. & Snijders, T. A. B. Estimation and Prediction for Stochastic Blockstructures. J. American Statistical Ass.96, 1077\u20131087 (2001).<\/section>\n<\/li>\n
  136. \n
    Girvan, M. & Newman, M. E. J. Community structure in social and biological networks. Proceedings of the National Academy of Sciences99, 7821 \u20137826 (2002).<\/section>\n<\/li>\n
  137. \n
    Schaub, M. T., Delvenne, J.-C., Rosvall, M. & Lambiotte, R. The many facets of community detection in complex networks. Appll. Network sci.2, 4 (2017).<\/section>\n<\/li>\n
  138. \n
    Cecchini, G. & Pikovsky, A. et al. Impact of local network characteristics on network reconstruction. Physical Review E.103, 022305 (2021).<\/section>\n<\/li>\n
  139. \n
    MacMahon, M. & Garlaschelli, D. Community Detection for Correlation Matrices. Phys. Rev. X.5, 021006 (2015).<\/section>\n<\/li>\n
  140. \n
    Masuda, N., Kojaku, S. & Sano, Y. Configuration model for correlation matrices preserving the node strength. Phys. Rev. E.98, 012312 (2018).<\/section>\n<\/li>\n
  141. \n
    Medaglia, J. D., Zurn, P., Sinnott-Armstrong, W. & Bassett, D. S. Mind control as a guide for the mind. Nature Human Behaviour.1, 1\u20138 (2017).<\/section>\n<\/li>\n
  142. \n
    Avella-Medina,  M., Parise, F., Schaub, M. & Segarra, S. Centrality measures for  graphons: Accounting for uncertainty in networks. IEEE Transactions on Network Science and Engineering (2018).<\/section>\n<\/li>\n<\/ol>\n

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