{"id":19788,"date":"2020-05-23T22:26:04","date_gmt":"2020-05-23T14:26:04","guid":{"rendered":"https:\/\/swarma.org\/?p=19788"},"modified":"2020-05-23T22:26:04","modified_gmt":"2020-05-23T14:26:04","slug":"er%e9%9a%8f%e6%9c%ba%e5%9b%be%e6%a8%a1%e5%9e%8b-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=19788","title":{"rendered":"ER\u968f\u673a\u56fe\u6a21\u578b | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\u968f\u673a\u56fe(random graph)<\/span><\/strong>\uff0c\u987e\u540d\u601d\u4e49\uff0c\u662f\u7531\u968f\u673a\u8fc7\u7a0b\u4ea7\u751f\u7684\u56fe\uff0c\u5177\u6709\u4e0d\u786e\u5b9a\u6027\u3002\u8fd9\u4e00\u7406\u8bba\u5904\u4e8e\u56fe\u8bba\u548c\u6982\u7387\u8bba\u7684\u4ea4\u53c9\u5730\u5e26\uff0c\u4e3b\u8981\u7814\u7a76\u7ecf\u5178\u968f\u673a\u56fe\u7684\u6027\u8d28\u3002\u4ece\u4efb\u4e00\u8282\u70b9\u51fa\u53d1\uff0c\u6309\u4e0d\u7ecf\u8fc7\u91cd\u590d\u8282\u70b9\u7684\u89c4\u5219\uff0c\u53ef\u968f\u673a\u8d70\u904d\u6240\u6709\u8282\u70b9\u7684\u56fe\u79f0\u4e3a\u968f\u673a\u54c8\u5bc6\u987f\u56fe\u3002\u4ece\u4efb\u4e00\u8282\u70b9\u51fa\u53d1\uff0c\u6309\u4e0d\u8fc7\u91cd\u590d\u8fb9\u7684\u89c4\u5219\uff0c\u53ef\u968f\u673a\u8d70\u904d\u6240\u6709\u8fb9\u800c\u56de\u5230\u51fa\u53d1\u70b9\u7684\u56fe\u79f0\u4e3a\u968f\u673a\u53ef\u8ff9\u56fe\u3002\u7b80\u5355\u7406\u89e3\uff0c\u968f\u673a\u56fe\u662f\u4f7f\u7528\u4e00\u4e9b\u89c4\u5219\u800c\u968f\u673a\u4ea7\u751f\u7684\u56fe\u3002ER\u968f\u673a\u56fe\u6a21\u578b\uff0c\u5c31\u662f\u4e00\u79cd\u63d0\u4f9b\u4e86\u4e00\u79cd\u89c4\u5219\uff0c\u6309\u7167\u8fd9\u79cd\u89c4\u5219\u6765\u4ea7\u751f\u968f\u673a\u56fe\u3002<\/span><\/p>\n

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ER\u968f\u673a\u56fe\u6a21\u578b\uff08Erd\u0151s\u2013R\u00e9nyi model\uff09\u6709\u4e24\u4e2a\u3002\u5176\u540d\u5b57\u6e90\u4e8e\u6700\u65e9\u63d0\u51fa\u4e0a\u8ff0\u6a21\u578b\u4e4b\u4e00\u7684\u6570\u5b66\u5bb6\u4fdd\u5c14\u00b7\u5384\u591a\u65af\uff08Paul Erd\u0151s\uff09\u548c\u963f\u5c14\u5f17\u70c8\u5fb7\u00b7\u745e\u5229\uff08Alfr\u00e9d R\u00e9nyi\uff09\uff0c\u4ed6\u4eec\u57281959\u5e74\u9996\u6b21\u63d0\u51fa\u4e86\u5176\u4e2d\u4e00\u4e2a\u6a21\u578b\uff0c\u51e0\u4e4e\u5728\u540c\u65f6\u671f\uff0c\u57c3\u5fb7\u52a0\u00b7<\/span>\u5409\u5c14\u4f2f\u7279\uff08Edgar Gilbert\uff09\u72ec\u7acb\u63d0\u51fa\u4e86\u53e6\u5916\u4e00\u4e2a\u6a21\u578b\u3002<\/span><\/p>\n


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\u4f8b\u5982\uff0c\u5728G(3\uff0c2)\u6a21\u578b\u4e2d\uff0c\u4e09\u4e2a\u9876\u70b9\u548c\u4e24\u4e2a\u8fb9\u53ef\u4ee5\u6784\u6210\u7684\u4e09\u4e2a\u53ef\u80fd\u7684\u56fe\uff0c\u6bcf\u4e00\u4e2a\u90fd\u4ee51\/3\u7684\u6982\u7387\u5305\u542b\u5728\u5185\u3002<\/span><\/p>\n


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2.\u5177\u6709\u56fa\u5b9a\u8282\u70b9\u548c\u8fde\u8fb9\u6982\u7387\u7684ER\u968f\u673a\u56fe\u6a21\u578b G(n,p)<\/span><\/section>\n
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\u66f4\u8fdb\u4e00\u6b65\u5730\u6765\u8bf4\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5229\u7528\u5b9e\u9645\u7f51\u7edc\u4e0e\u6a21\u578b\u7684\u5de8\u5927\u5dee\u5f02\uff0c\u6765\u8bc6\u522b\u793e\u4ea4\u7f51\u7edc\u4e2d\u7684\u865a\u62df\u8d26\u6237\u3001AI\u8d26\u6237\uff0c\u627e\u5230\u7f51\u7edc\u4e2d\u7684\u5f02\u5e38\u60c5\u51b5\u3002\u66f4\u76f4\u63a5\u7684\u5546\u4e1a\u5e94\u7528\u662f\u5728\u5e7f\u544a\u4e2d\uff0c\u5229\u7528\u968f\u673a\u56fe\u6a21\u578b\u53ef\u4ee5\u53d1\u73b0\u7528\u6237\u4e2d\u7684\u5546\u4e1a\u8d8b\u52bf\u6216\u8bc6\u522b\u7528\u6237\u7279\u5f81\uff0c\u4ee5\u6b64\u5b9e\u73b0\u66f4\u7cbe\u51c6\u7684\u5e7f\u544a\u63a8\u9001\u3002<\/span><\/p>\n


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\u4fdd\u5c14\u00b7\u5384\u591a\u65af Paul Erd\u0151s<\/span><\/strong><\/span><\/section>\n

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\u963f\u5c14\u5f17\u70c8\u5fb7\u00b7\u745e\u5229 Alfr\u00e9d R\u00e9nyi<\/span><\/strong><\/span><\/p>\n


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\u56fe4\uff1aAlfr\u00e9d R\u00e9nyi<\/strong><\/strong>
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N Is a Number: A Portrait of Paul Erd\u0151s<\/span><\/p>\n


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\u56fe5\uff1a<\/strong>N Is a Number\u5267\u7167<\/strong><\/p>\n


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N Is a Number: A Portrait of Paul Erd\u0151s\u64ad\u653e\u5730\u5740\uff1a<\/section>\n
https:\/\/www.bilibili.com\/video\/BV1ns411E74Y<\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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[1]Erd\u0151s, P.; R\u00e9nyi, A. (1959). “On Random Graphs. I”. Publicationes Mathematicae 6: 290\u2013297. http:\/\/www.renyi.hu\/~p_erdos\/1959-11.pdf.<\/span><\/p>\n

[2]Bollob\u00e1s, B. (2001). Random Graphs (2nd ed.). Cambridge University Press. “.ISBN 0-521-79722-5”<\/span><\/p>\n

[3]E.N. Gilbert (1959). “Random Graphs”. Annals of Mathematical Statistics 30 (4): 1141\u20131144. “.doi:10.1214\/aoms\/1177706098”<\/span><\/p>\n

[4]Newman, Mark. E. J.; Strogatz, S. H.; Watts, D. J. (2001). “Random graphs with arbitrary degree distributions and their applications”. Physical Review E 64: 026118. “.doi:10.1103\/PhysRevE.64.026118 .arxiv:cond-mat\/0007235 .bibcode:2001PhRvE..64b6118N”, Eq. (1)<\/span><\/p>\n

[5]Erd\u0151s, P.; R\u00e9nyi, A. (1960). “On the evolution of random graphs”. Magyar Tudom\u00e1nyos Akad\u00e9mia Matematikai Kutat\u00f3 Int\u00e9zet\u00e9nek K\u0151zlem\u00e9nyei [Publications of the Mathematical Institute of the Hungarian Academy of Sciences] 5: 17\u201361. http:\/\/www.renyi.hu\/~p_erdos\/1960-10.pdf. <\/span><\/p>\n

[6]Matula, David W. (February 1972). “The employee party problem”. Notices of the American Mathematical Society 19: A-382.<\/span><\/p>\n

[7]Bollob\u00e1s, B.; Erd\u0151s, P. (1976). “Cliques in Random Graphs”. Mathematical Proceedings of the Cambridge Philosophical Society 80 (3): 419\u2013427. “.doi:10.1017\/S0305004100053056 .bibcode:1976MPCPS..80..419B”<\/span><\/p>\n


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\u5546\u52a1\u5408\u4f5c\u53ca\u6295\u7a3f\u8f6c\u8f7d\uff5cswarma@swarma.org
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