{"id":23222,"date":"2021-01-11T21:09:43","date_gmt":"2021-01-11T13:09:43","guid":{"rendered":"https:\/\/swarma.org\/?p=23222"},"modified":"2021-01-11T21:09:43","modified_gmt":"2021-01-11T13:09:43","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e9%a1%b6%e7%82%b9%ef%bc%88%e7%bd%91%e7%bb%9c%e7%a7%91%e5%ad%a6%ef%bc%89-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=23222","title":{"rendered":"\u4ec0\u4e48\u662f\u9876\u70b9\uff08\u7f51\u7edc\u79d1\u5b66\uff09 | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"

\u201c\u96c6\u667a\u767e\u79d1\u7cbe\u9009\u201d\u662f\u4e00\u4e2a\u957f\u671f\u4e13\u680f\uff0c\u6301\u7eed\u4e3a\u5927\u5bb6\u63a8\u9001\u590d\u6742\u6027\u79d1\u5b66\u76f8\u5173\u7684\u57fa\u672c\u6982\u5ff5\u548c\u8d44\u6e90\u4fe1\u606f\u3002\u4f5c\u4e3a\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u5f00\u6e90\u79d1\u5b66\u9879\u76ee\uff0c\u96c6\u667a\u767e\u79d1\u5e0c\u671b\u6253\u9020\u590d\u6742\u6027\u79d1\u5b66\u9886\u57df\u6700\u5168\u9762\u7684\u767e\u79d1\u5168\u4e66\uff0c\u6b22\u8fce\u5bf9\u590d\u6742\u6027\u79d1\u5b66\u611f\u5174\u8da3\u3001\u70ed\u7231\u77e5\u8bc6\u6574\u7406\u548c\u5206\u4eab\u7684\u670b\u53cb\u52a0\u5165\uff01


\u672c\u6587\u662f\u5bf9\u96c6\u667a\u767e\u79d1\u4e2d\u201c\u9876\u70b9\u201d\u8bcd\u6761\u7684\u6458\u5f55\uff0c\u53c2\u8003\u8d44\u6599\u53ca\u76f8\u5173\u8bcd\u6761\u8bf7\u53c2\u9605\u767e\u79d1\u8bcd\u6761\u539f\u6587\u3002


\u672c\u8bcd\u6761\u7531\u96c6\u667a\u4ff1\u4e50\u90e8\u4f17\u5305\u751f\u4ea7\uff0c\u96be\u514d\u5b58\u5728\u7eb0\u6f0f\u548c\u95ee\u9898\uff0c\u6b22\u8fce\u5927\u5bb6\u7559\u8a00\u53cd\u9988\u6216\u8005\u524d\u5f80\u5bf9\u5e94\u7684\u767e\u79d1\u8bcd\u6761\u9875\u9762\u8fdb\u884c\u4fee\u6539\uff0c\u4e00\u7ecf\u4fee\u6539\uff0c\u53ef\u4ee5\u83b7\u5f97\u5bf9\u5e94\u7684\u79ef\u5206\u5956\u52b1\u5662\uff01


\u76ee\u5f55


\u4e00\u3001\u4ec0\u4e48\u662f\u9876\u70b9\uff1f
\u4e8c\u3001\u9876\u70b9\u7c7b\u578b
\u4e09\u3001\u76f8\u5173\u8d44\u6e90\u63a8\u8350
\u56db\u3001\u96c6\u667a\u767e\u79d1\u8bcd\u6761\u5fd7\u613f\u8005\u62db\u52df
\u9876\u70b9_Vertex\uff1ahttps:\/\/wiki.swarma.org\/index.php?title=\u9876\u70b9_Vertex





1. \u4ec0\u4e48\u662f\u9876\u70b9\uff1f




\u5728\u6570\u5b66\u4e0a\uff0c\u66f4\u5177\u4f53\u5730\u8bf4\u5728\u56fe\u8bba\u4e2d\uff0c\u56fe\u8fd9\u4e00\u62bd\u8c61\u5bf9\u8c61\u7684\u57fa\u672c\u7ec4\u6210\u5355\u5143\u662f\u9876\u70b9\u6216\u8282\u70b9\uff1a\u65e0\u5411\u56fe\u7531\u4e00\u7ec4\u9876\u70b9\u548c\u4e00\u7ec4\u8fb9\uff08\u6bcf\u6761\u8fb9\u7531\u4e00\u5bf9\u9876\u70b9\u7ec4\u6210\uff0c\u4e0d\u533a\u5206\u8fd9\u4fe9\u9876\u70b9\u7684\u987a\u5e8f\uff09\u7ec4\u6210\uff0c\u800c\u6709\u5411\u56fe\u7531\u4e00\u7ec4\u9876\u70b9\u548c\u4e00\u7ec4\u5f27\uff08\u6bcf\u6761\u5f27\u7531\u4e00\u5bf9\u9876\u70b9\u7ec4\u6210\uff0c\u533a\u5206\u8fd9\u4fe9\u9876\u70b9\u7684\u987a\u5e8f\uff09\u7ec4\u6210\u3002\u5728\u62bd\u8c61\u56fe\u7684\u56fe\u793a\u4e2d\uff0c\u4e00\u822c\u800c\u8a00\uff0c\u5e26\u6807\u6ce8\u7684\u5706\u5708\u8868\u793a\u9876\u70b9\uff0c\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u7684\u76f4\u7ebf\u6216\u7bad\u5934\u8868\u793a\u8fb9\u3002\u76f4\u7ebf\u7528\u4e8e\u8868\u793a\u65e0\u5411\u56fe\u7684\u8fb9\uff0c\u7bad\u5934\u8868\u793a\u6709\u5411\u56fe\u7684\u8fb9\u3002<\/p>\n

\u4ece\u56fe\u8bba\u7684\u89c2\u70b9\u6765\u770b\uff0c\u9876\u70b9\u88ab\u89c6\u4e3a\u6ca1\u6709\u5c5e\u6027\u4e14\u4e0d\u53ef\u5206\u5272\u7684\u5bf9\u8c61\u3002\u65e0\u8bba\u8fd9\u4e9b\u9876\u70b9\u6240\u7ec4\u6210\u7684\u56fe\u6765\u81ea\u4ec0\u4e48\u6837\u7684\u5e94\u7528\u573a\u666f\uff0c\u65e0\u8bba\u5728\u8fd9\u4e9b\u5e94\u7528\u573a\u666f\u4e2d\uff0c\u9876\u70b9\u6240\u8868\u793a\u7684\u5bf9\u8c61\u53c8\u6709\u4ec0\u4e48\u989d\u5916\u7684\u7ed3\u6784\u3002\u4f8b\u5982: \u8ba1\u7b97\u673a\u79d1\u5b66\u9886\u57df\u4e2d\u7684\u8bed\u4e49\u7f51\u7edc\uff0c\u5c31\u53ef\u4ee5\u62bd\u8c61\u4e3a\u56fe\uff0c\u5176\u9876\u70b9\u8868\u793a\u6982\u5ff5\u6216\u5bf9\u8c61\u7684\u7c7b\u3002<\/p>\n

\u82e5\u56fe\u5305\u542b\u7531\u9876\u70b9\u548c\u7ec4\u6210\u7684\u8fb9\uff0c\u5219\u79f0\u9876\u70b9\u90bb\u63a5\u4e8eadjacent to\u9876\u70b9;\u7531\u6240\u6709\u90bb\u63a5\u4e8e\u7684\u9876\u70b9\u800c\u7ec4\u6210 \u7684\u56fe\uff0c\u88ab\u79f0\u4e3a\u8fd9\u4e9b\u9876\u70b9\u7684\u5bfc\u51fa”’\u5b50\u56feinduced subgraph”’\uff0c\u5b83\u4e5f\u88ab\u79f0\u4e3a\u9876\u70b9\u7684”’\u90bb\u57df neighborhood”’\u3002<\/p>\n





2. \u9876\u70b9\u7c7b\u578b


<\/p>\n

\u5728\u62bd\u8c61\u56fe\u4e2d\uff0c\u9876\u70b9\u7684\u5ea6 degree\uff0c\u8bb0\u4f5c\uff0c\u662f\u6240\u6709\u5173\u8054\u4e8e\u7684\u8fb9\u7684\u6570\u91cf\u3002\u5ea6\u4e3a0\u7684\u9876\u70b9\u88ab\u79f0\u4f5c\u5b64\u7acb\u9876\u70b9 isolated vertex\uff0c\u8fd9\u6837\u7684\u9876\u70b9\u4e0d\u662f\u4efb\u4f55\u8fb9\u7684\u7aef\u70b9(\u5982\u56fe2\u6240\u793a\uff0c\u8fd9\u4e00\u62bd\u8c61\u56fe\u4e2d\u542b\u6709\u4e00\u4e2a\u5b64\u7acb\u9876\u70b9)
\u5ea6\u4e3a1\u7684\u9876\u70b9\u88ab\u79f0\u4e3a\u53f6\u9876\u70b9 leaf vertex\uff0c\u4e5f\u79f0\u53f6\u5b50\u9876\u70b9\u3001\u53f6\u8282\u70b9\u3001\u60ac\u6302\u9876\u70b9 pendant vertex\u3002
\u5728\u6709\u5411\u56fe\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u8fb9\u7684\u65b9\u5411\uff0c\u628a\u9876\u70b9\u7684\u5ea6\u5206\u4e3a\u51fa\u5ea6 outdegree(\u4e5f\u79f0\u51fa\u6b21\u6570)\uff0c\u8bb0\u4f5c\u548c\u5165\u5ea6 indegree(\u4e5f\u79f0\u5165\u6b21\u6570)\uff0c\u8bb0\u4f5c\u3002\u4e00\u4e2a\u9876\u70b9\u7684\u51fa\u5ea6\u6307\u7684\u662f\uff0c\u6240\u6709\u4ece\u8fd9\u4e2a\u9876\u70b9\u51fa\u53d1\uff0c\u8fde\u63a5\u5176\u4ed6\u9876\u70b9\u7684\u7bad\u5934\u7684\u6570\u91cf\u3002\u4e0e\u6b64\u76f8\u53cd\uff0c\u4e00\u4e2a\u9876\u70b9\u7684\u5165\u5ea6\u6307\u7684\u662f\uff0c\u6240\u6709\u4ece\u5176\u4ed6\u9876\u70b9\u51fa\u53d1\uff0c\u8fde\u63a5\u5230\u8fd9\u4e2a\u9876\u70b9\u7684\u7bad\u5934\u7684\u6570\u91cf\u3002\u5728\u6709\u5411\u56fe\u4e2d\uff0c\u6709\u53ef\u80fd\u51fa\u73b0\u4e24\u79cd\u9876\u70b9\uff1a\u6e90\u9876\u70b9 source vertex \u548c\u6c47\u9876\u70b9 sink vertex\u3002\u524d\u8005\u6307\u5165\u5ea6\u4e3a0\u7684\u9876\u70b9\uff0c\u540e\u8005\u6307\u51fa\u5ea6\u4e3a0\u7684\u9876\u70b9\u3002
\u82e5\u4e00\u4e2a\u9876\u70b9\u7684\u90bb\u57df\u6070\u597d\u80fd\u6784\u6210\u56e2 clique\uff0c\u5373\u8fd9\u4e2a\u9876\u70b9\u90bb\u57df\u4e2d\u7684\u4efb\u610f\u4e24\u4e2a\u9876\u70b9\u90fd\u662f\u76f8\u90bb\u7684\uff0c\u90a3\u4e48\u8fd9\u4e2a\u9876\u70b9\u88ab\u79f0\u4e3a\u5355\u7eaf\u5f62\u9876\u70b9 simplicial vertex\uff0c\u4e5f\u8bd1\u4e3a\u5355\u7eaf\u9876\u70b9\u3002\u4e0e\u6240\u6709\u5176\u4ed6\u9876\u70b9\u76f8\u90bb\u7684\u9876\u70b9\uff0c\u88ab\u79f0\u4e3a\u6cdb\u9876\u70b9 universal vertex\u3002
\u82e5\u79fb\u9664\u67d0\u4e00\u9876\u70b9\uff08\u548c\u6240\u6709\u4ee5\u8fd9\u4e2a\u9876\u70b9\u4e3a\u7aef\u70b9\u7684\u8fb9\uff09\u540e\uff0c\u56fe\u88ab\u5206\u79bb\u4e3a\u82e5\u5e72\u4e2a\u5f7c\u6b64\u4e92\u4e0d\u76f8\u8fde\u7684\u5b50\u56fe\uff0c\u90a3\u4e48\u8fd9 \u4e00\u9876\u70b9\u5c31\u88ab\u79f0\u4e3a\u5272\u9876\u70b9 cut vertex;\u7531\u5272\u9876\u70b9\u6784\u6210\u7684\u96c6\u5408\u88ab\u79f0\u4e3a\u9876\u70b9\u5206\u79bb\u96c6\u3002\u82e5\u4e00\u4e2a\u8fde\u901a\u56fe\u88ab\u79fb\u9664\u5c11\u4e8eK\u4e2a\u9876\u70b9\u540e\uff0c\u603b\u80fd\u4fdd\u6301\u8fde\u901a\uff0c\u90a3\u4e48\u8fd9\u4e2a\u56fe\u88ab\u79f0\u4e3aK-\u9876\u70b9\u8fde\u901a\u56fe\u3002\u7531\u4e24\u4e24\u4e0d\u76f8\u90bb\u7684\u9876\u70b9\u6240\u6784\u6210\u7684\u96c6\u5408\uff0c\u88ab\u79f0\u4e3a\u72ec\u7acb\u96c6\u3002\u7531\u56fe\u4e2d\u6bcf\u6761\u8fb9\u7684\u4e00\u4e2a\u6216\u4e24\u4e2a\u7aef\u70b9\u6240\u6784\u6210\u7684\u96c6\u5408\uff0c\u88ab\u79f0\u4e3a\u9876\u70b9\u8986\u76d6\u3002\u56fe\u7684\u9876\u70b9\u7a7a\u95f4\u662f\u5411\u91cf\u7a7a\u95f4\uff0c\u5b83\u7684\u57fa\u5411\u91cf\u4e0e\u56fe\u7684\u9876\u70b9\u76f8\u5bf9\u5e94\u3002
\u5982\u679c\u4e00\u4e2a\u56fe\u5177\u6709\u5c06\u4efb\u4f55\u9876\u70b9\u6620\u5c04\u5230\u4efb\u4f55\u5176\u4ed6\u9876\u70b9\u7684\u5bf9\u79f0\u6027\uff0c\u5219\u8be5\u56fe\u662f\u9876\u70b9\u4f20\u9012\u7684\u3002
\u5982\u679c\u4e00\u4e2a\u56fe\u4e0a\u5b58\u5728\u67d0\u79cd\u81ea\u540c\u6784\u6620\u5c04automorphism\uff0c\u80fd\u628a\u56fe\u4e2d\u4efb\u610f\u4e00\u4e2a\u9876\u70b9\u6620\u5c04\u4e3a\u56fe\u4e2d\u7684\u67d0\u4e2a\u5176\u4ed6\u9876\u70b9 \uff0c\u540c\u65f6\u4fdd\u6301\u8fb9\u4e0d\u53d8\uff0c\u5373\u82e5\u9876\u70b9\u76f8\u90bb\uff0c\u90a3\u4e48\u9876\u70b9\u548c\u4e5f\u76f8\u90bb\uff0c\u90a3\u4e48\u6211\u4eec\u8ba4\u4e3a\u8fd9\u4e2a\u56fe\u662f\u9876\u70b9\u4f20\u9012\u7684\uff0c\u8fd9\u6837\u7684\u56fe\u5177\u6709\u67d0\u79cd\u76f8\u5e94\u7684\u5bf9\u79f0\u6027\u8d28\u3002
\u5728\u56fe\u8ba1\u6570\u6216\u8005\u56fe\u540c\u6784\u7684\u8bed\u5883\u4e2d\uff0c\u82e5\u56fe\u4e2d\u7684\u9876\u70b9\u90fd\u662f\u65e0\u6807\u6ce8\u7684\u9876\u70b9\uff0c\u5219\u53ef\u4ee5\u4e0d\u7528\u8003\u8651\u4e0a\u9762\u90a3\u6837\u989d\u5916\u4fe1\u606f\u7684\u5f71\u54cd\u3002\u53ea\u8981\u4e24\u4e2a\u56fe\u4e4b\u95f4\u5b58\u5728\u9876\u70b9\u4e4b\u95f4\u7684\u6620\u5c04\uff0c\u4f7f\u5f97\u539f\u6765\u8fde\u901a\u7684\u9876\u70b9\uff0c\u5728\u6620\u5c04\u4e4b\u540e\u4f9d\u7136\u8fde\u901a\uff0c\u5c31\u53ef\u4ee5\u8bf4\u8fd9\u4e24\u4e2a\u56fe\u662f\u540c\u6784\u7684\u3002
\u56fe\u7684\u9876\u70b9\u7c7b\u4f3c\u4e8e\u4f46\u4e0d\u7b49\u540c\u4e8e(\u9ad8\u7ef4)\u591a\u9762\u4f53\u7684\u9876\u70b9\u3002\u4f46\u591a\u9762\u4f53\u7684\u9876\u70b9\u6709\u989d\u5916\u7684\u7ed3\u6784(\u51e0\u4f55\u4f4d\u7f6e)\uff0c\u5728\u56fe\u8bba\u4e2d\u672a\u80fd\u88ab\u5047\u5b9a\u5b58\u5728\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4f5c\u4e3a\u6982\u5ff5\uff0c\u56fe\u7684\u9876\u70b9\u6bd4\u591a\u9762\u4f53\u7684\u9876\u70b9\uff0c\u8981\u66f4\u62bd\u8c61\u3002\u591a\u9762\u4f53\u7684\u9aa8\u67b6\u6784\u6210\u4e00\u4e2a\u56fe\uff0c\u5176\u9876\u70b9\u662f\u591a\u9762\u4f53\u7684\u9876\u70b9\uff0c\u4f46\u591a\u9762\u4f53\u7684\u9876\u70b9\u6709\u65e0\u6cd5\u5728\u56fe\u8bba\u4e2d\u5047\u5b9a\u5b58\u5728\u7684\u5176\u4ed6\u7ed3\u6784(\u51e0\u4f55\u4f4d\u7f6e) \u3002\u591a\u9762\u4f53\u4e2d\u9876\u70b9\u7684\u9876\u70b9\u56fe\u5f62\u7c7b\u4f3c\u4e8e\u56fe\u4e2d\u9876\u70b9\u7684\u90bb\u57df\u3002





3. \u76f8\u5173\u8d44\u6e90\u63a8\u8350



<\/p>\n

\u8bfe\u7a0b\u63a8\u8350
\u6f2b\u8c08\u56fe\u8bba\u7684\u8d77\u6e90\u3001\u53d1\u5c55\u4e0e\u5e94\u7528
\u672c\u8bfe\u7a0b\u4e2d\uff0c\u4ecb\u7ecd\u4e86\u56fe\u8bba\u4e2d\u7684\u57fa\u672c\u6982\u5ff5\u548c\u7f51\u7edc\u79d1\u5b66\u4f7f\u7528\u7684\u5de5\u5177\uff0c\u53ef\u4ee5\u5e2e\u52a9\u8ba4\u8bc6\u771f\u5b9e\u7f51\u7edc\u7684\u5173\u952e\u6027\u8d28\u3002





\u8bfe\u7a0b\u63a8\u8350\uff1a\u6f2b\u8c08\u56fe\u8bba\u7684\u8d77\u6e90\u3001\u53d1\u5c55\u4e0e\u5e94\u7528https:\/\/campus.swarma.org\/course\/1745





4. \u767e\u79d1\u9879\u76ee\u5fd7\u613f\u8005\u62db\u52df




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\u63a8\u8350\u9605\u8bfb\u4ec0\u4e48\u662f\u4eba\u5de5\u793e\u4f1a\uff1f| \u96c6\u667a\u767e\u79d1<\/a>

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\u4ec0\u4e48\u662f\u5143\u80de\u81ea\u52a8\u673a\uff1f| \u96c6\u667a\u767e\u79d1<\/a>
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\u4ec0\u4e48\u662f\u975e\u7ebf\u6027\u7cfb\u7edf | \u96c6\u667a\u767e\u79d1<\/a>

\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/a>



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