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class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_4-4-1024x253.png\" alt=\"\" class=\"wp-image-20378\" width=\"800\" srcset=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_4-4-1024x253.png 1024w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_4-4-300x74.png 300w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_4-4-768x190.png 768w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_4-4-18x4.png 18w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_4-4.png 1481w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\">\u88681 \u300a\u6587\u6d77\u300b\u5b57\u578b\u89e3\u91ca\u4e3e\u4f8b<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>\u5982\u524d\u6587\u6240\u8ff0\u300a\u6587\u6d77\u300b\u4e2d\u4e3b\u8981\u5305\u542b\u516b\u79cd\u6784\u5b57\u89e3\u91ca\u5173\u7cfb\uff0c\u4f46\u6211\u4eec\u5728\u6784\u5efa\u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u65f6\u5bf9\u4e8e\u8fd9\u4e9b\u5173\u7cfb\u5e76\u4e0d\u4f5c\u533a\u5206\uff0c\u5c06\u5176\u5408\u5e76\u4e3a\u4e00\u79cd\u5173\u7cfb\uff0c\u5373\u89e3\u91ca\u5173\u7cfb\uff1a\u88ab\u89e3\u91ca\u7684\u5b57\u548c\u7528\u4e8e\u89e3\u91ca\u7684\u5b57\uff08\u6784\u5b57\uff09\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u6211\u4eec\u6784\u5efa\u7684\u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u662f\u4e00\u4e2a\u6709\u5411\u56fe\uff0c\u6bcf\u4e00\u6761\u8fb9\u7684\u65b9\u5411\u90fd\u662f\u4ece\u6784\u5b57\u6307\u5411\u88ab\u89e3\u91ca\u5b57\uff0c\u8fd9\u6837\u4e0a\u8ff0\u89e3\u91ca\u5173\u7cfb\u7684\u4f8b\u5b50\u4e2d\u7684ABC\u4e09\u4e2a\u5b57\u5728\u5b57\u5178\u7f51\u7edc\u4e2d\u5c31\u5f62\u6210\u4e86\u4e24\u6761\u6709\u5411\u8fb9B\u2192A\u548cC\u2192A\uff0c\u8868\u793aA\u7684\u89e3\u91ca\u4e2d\u6709B\u548cC\uff1b\u5f53\u7136ABC\u90fd\u53ef\u80fd\u51fa\u73b0\u5728\u5176\u4ed6\u5b57\u7684\u89e3\u91ca\u4e2d\uff0c\u5373\u5b83\u4eec\u90fd\u53ef\u80fd\u6307\u5411\u5176\u4ed6\u7684\u8282\u70b9\u3002\u6839\u636e\u8fd9\u79cd\u89e3\u91ca\u5173\u7cfb\uff0c\u300a\u6587\u6d77\u300b\u4e2d\u6240\u6709\u7684\u897f\u590f\u5b57\u5c31\u6784\u6210\u4e86\u4e00\u4e2a\u7f51\u7edc\uff0c\u5373\u5b57\u5178\u7f51\u7edc\uff0c\u7f51\u7edc\u4e2d\u7684\u8282\u70b9\u662f\u897f\u590f\u5b57\uff0c\u8fb9\u4e3a\u89e3\u91ca\u5173\u7cfb\u3002\u901a\u8fc7\u5206\u6790\u8282\u70b9\u7684\u53ef\u8fbe\u5173\u7cfb\u4ee5\u53ca\u7f51\u7edc\u4e2d\u7684\u5faa\u73af\u5173\u7cfb\u6211\u4eec\u53ef\u4ee5\u627e\u51fa\u897f\u590f\u5b57\u4e2d\u7684\u57fa\u672c\u5b57\uff1b\u901a\u8fc7\u8ba1\u7b97\u6240\u6709\u897f\u590f\u5b57\u5230\u57fa\u672c\u5b57\u96c6\u5408\u7684\u8ddd\u79bb\uff0c\u6211\u4eec\u80fd\u591f\u5206\u6790\u300a\u6587\u6d77\u300b\u4e2d\u897f\u590f\u5b57\u89e3\u91ca\u5173\u7cfb\u7684\u5c42\u6b21\u7ed3\u6784\uff0c\u4ece\u800c\u6709\u53ef\u80fd\u4e3a\u73b0\u4ee3\u4eba\u5b66\u4e60\u897f\u590f\u6587\u63d0\u4f9b\u4e00\u6761\u4f18\u5316\u7684\u5b66\u4e60\u8def\u5f84\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u7b80\u8981\u4ecb\u7ecd\u4e00\u4e0b\u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u7684\u6784\u5efa\uff08\u7531\u4e8e\u7f51\u7edc\u5206\u6790\u5e7f\u6cdb\u4f7f\u7528\u56fe\u7406\u8bba\u548c\u56fe\u7b97\u6cd5\uff0c\u56e0\u6b64\u672c\u6587\u4e2d\u56fe\u548c\u7f51\u7edc\u7684\u542b\u4e49\u662f\u7b49\u4ef7\u7684\uff09\u3002<\/p>\n\n\n\n<p>\u5b57\u5178\u7f51\u7edc\u662f\u4e00\u4e2a\u6709\u5411\u56fe<em>G=<\/em>\uff08<em>V,E<\/em>\uff09\uff0c\u5176\u4e2d<em>G<\/em>\u8868\u793a\u5b57\u5178\u7f51\u7edc\u6216\u56fe\uff0c<em>V<\/em>\u8868\u793a\u56fe\u4e2d\u7684\u8282\u70b9\u96c6\u5408\uff0c\u4e00\u4e2a\u8282\u70b9\u5bf9\u5e94\u5b57\u5178\u4e2d\u7684\u4e00\u4e2a\u5b57\uff0c<em>E<\/em>\u8868\u793a\u8282\u70b9\u4e4b\u95f4\u6784\u6210\u7684\u8fb9\u7684\u96c6\u5408\u3002\uff08<em>v<\/em>1<em>,v<\/em>2\uff09\u8868\u793a\u56fe<em>G<\/em>\u4e2d\u7684\u4e00\u6761\u6709\u5411\u8fb9\uff08<em>v<\/em>1<em>,v<\/em>2\uff09\u2208<em>E<\/em>\uff0c<em>v<\/em>1\u548c<em>v<\/em>2\u4e3a\u8be5\u8fb9\u7684\u4e24\u4e2a\u8282\u70b9\uff0c\u8868\u793a\u5b57\u5178\u4e2d\u7684\u4e24\u4e2a\u5b57\uff0c\u8fb9\u7684\u65b9\u5411\u4e3a\u4ece<em>v<\/em>1\u6307\u5411<em>v<\/em>2\uff0c\u8868\u793a\u5b57\u5178\u5b9a\u4e49\u4e2d<em>v<\/em>1\u51fa\u73b0\u5728<em>v<\/em>2\u7684\u5b9a\u4e49\u4e2d\uff1b\u56feG\u4e2d\u53ef\u80fd\u6709\u591a\u6761\u6709\u5411\u8fb9\u6307\u5411<em>v<\/em>2\uff0c\u56e0\u4e3a\u5b57\u5178\u4e2d\u4e00\u4e2a\u5b57\u5f80\u5f80\u7531\u591a\u4e2a\u5b57\u6765\u89e3\u91ca\uff1b<em>v<\/em>1\u9664\u4e86\u6709\u6307\u5411<em>v<\/em>2\u7684\u8fb9\u8fd8\u53ef\u80fd\u6709\u591a\u6761\u6307\u5411\u5176\u4ed6\u8282\u70b9\u7684\u8fb9\uff0c\u56e0\u4e3a\u4e00\u4e2a\u5b57\u53ef\u80fd\u4f1a\u51fa\u73b0\u5728\u591a\u4e2a\u5b57\u7684\u89e3\u91ca\u4e2d\u3002\u6240\u4ee5\uff0c\u4e00\u4e2a\u7b80\u5355\u7684\u89e3\u91ca\u5173\u7cfb\u5c31\u8ba9\u51e0\u5343\u4e2a\u897f\u590f\u5b57\u7ec4\u6210\u56fe1\u6240\u793a\u7684\u5e9e\u5927\u800c\u4e14\u9519\u7efc\u590d\u6742\u7684\u7f51\u7edc\uff0c\u8fd9\u4e5f\u662f\u590d\u6742\u7f51\u7edc\u7684\u5171\u540c\u7279\u70b9\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u6784\u5efa\u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u65f6\uff0c\u4e3b\u8981\u9009\u62e9\u4e86\u300a\u6587\u6d77\u300b\u4e2d\u7684\u5b8c\u6574\u7684\u56db\u5b57\u89e3\u91ca\u8bcd\u6761\uff0c\u5373\u6bcf\u4e2a\u897f\u590f\u5b57\u90fd\u662f\u7531\u53e6\u5916\u4e24\u4e2a\u897f\u590f\u5b57\u89e3\u91ca\uff0c\u56e0\u6b64\u7f51\u7edc\u4e2d\u6bcf\u4e2a\u8282\u70b9\u7684\u5165\u5ea6\u90fd\u4e3a2\uff0c\u5982\u88682\u6240\u793a\u3002\u5176\u4e2d\uff0ctarget_id\u548csource_id\u5217\u6240\u5bf9\u5e94\u7684\u6570\u5b57\u662f\u897f\u590f\u5b57\u7684\u5b57\u5178\u5e8f\u53f7\uff0ctarget\u548csource\u5217\u5bf9\u5e94\u7684\u662f\u5177\u4f53\u7684\u897f\u590f\u5b57\uff1b\u6bcf\u4e24\u884c\u8868\u793a\u300a\u6587\u6d77\u300b\u4e2d\u7684\u4e00\u4e2a\u89e3\u91ca\u6761\u76ee\uff0c\u6bcf\u4e00\u884c\u8868\u793a\u5b57\u5178\u7f51\u7edc\u4e2d\u7684\u4e00\u6761\u6709\u5411\u8fb9\uff0c\u65b9\u5411\u90fd\u662f\u4ecesource\u8282\u70b9\u6307\u5411target\u8282\u70b9\u3002\u8fd9\u79cd\u683c\u5f0f\u7684\u6570\u636e\u80fd\u591f\u76f4\u63a5\u4f7f\u7528\u7f51\u7edc\u5206\u6790\u8f6f\u4ef6Gephi\u8fdb\u884c\u53ef\u89c6\u5316\uff0c\u5982\u56fe1\u6240\u793a\u3002\u6211\u4eec\u6784\u5efa\u7684\u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u603b\u5171\u5305\u62ec3,781\u4e2a\u8282\u70b9\uff08\u897f\u590f\u5b57\uff09\uff0c\u5176\u4e2d\u7684\u7eff\u8272\u533a\u57df\u5305\u542b2,970\u4e2a\u8282\u70b9\uff0c\u662f\u672c\u6587\u4e3b\u8981\u7814\u7a76\u7684\u5bf9\u8c61\uff0c\u5176\u4f59\u533a\u57df\u5305\u542b811\u4e2a\u8282\u70b9\uff0c\u540e\u7eed\u9664\u4e86\u53ef\u89c6\u5316\u4e4b\u5916\u7f51\u7edc\u5206\u6790\u90e8\u5206\u4e0d\u6d89\u53ca\u8fd9811\u4e2a\u8282\u70b9\u3002\u8fd9\u4e24\u90e8\u5206\u7684\u5206\u79bb\u4e3b\u8981\u662f\u56e0\u4e3a\uff081\uff09\u73b0\u5b58\u7684\u300a\u6587\u6d77\u300b\u5b57\u5178\u662f\u4e0d\u5b8c\u6574\u7684\uff0c\u6709\u4e9b\u8bcd\u6761\u7684\u89e3\u91ca\u7f3a\u5931\uff1b\uff082\uff09\u672c\u6587\u4e3b\u8981\u5173\u6ce8\u7684\u89e3\u91ca\u6a21\u5f0f\u4e3a\u5360\u5b57\u5178\u4e3b\u8981\u90e8\u5206\u7684\u201c\u56db\u5b57\u89e3\u91ca\u201d\u8bcd\u6761\uff0c\u8fd8\u6709\u4e00\u5c0f\u90e8\u5206\u4e0d\u7b26\u5408\u8fd9\u79cd\u6a21\u5f0f\u3002\u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u4e2d\u57fa\u672c\u5b57\u96c6\u6240\u4ee3\u8868\u76842,970\u4e2a\u8282\u70b9\u90e8\u5206\uff0c\u867d\u7136\u8282\u70b9\u6570\u5c11\u4e86\u4e00\u4e9b\uff0c\u4f46\u7f51\u7edc\u7ed3\u6784\u5b8c\u6574\uff0c\u80fd\u591f\u96c6\u4e2d\u53cd\u6620\u8be5\u5b57\u5178\u6587\u5b57\u5b9a\u4e49\u7684\u6a21\u5f0f\uff0c\u7814\u7a76\u7ed3\u8bba\u548c\u65b9\u6cd5\u80fd\u591f\u63a8\u5e7f\u5e94\u7528\u4e8e\u5206\u6790\u5176\u4ed6\u8bed\u8a00\u7684\u5b57\u5178\u5b9a\u4e49\u6a21\u5f0f\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_5-4-1024x366.png\" alt=\"\" class=\"wp-image-20379\" width=\"800\" srcset=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_5-4-1024x366.png 1024w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_5-4-300x107.png 300w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_5-4-768x274.png 768w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_5-4-18x6.png 18w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_5-4.png 1456w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\">\u88682 \u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u7684\u8fb9\u4e3e\u4f8b<\/p>\n\n\n\n<p>\uff08\u4e8c\uff09\u5b57\u5178\u7f51\u7edc\u7684\u53ef\u89c6\u5316<\/p>\n\n\n\n<p>\u590d\u6742\u7f51\u7edc\u5206\u6790\u7684\u6570\u636e\u89c4\u6a21\u5f80\u5f80\u6bd4\u8f83\u5927\uff0c\u6570\u636e\u4e4b\u95f4\u7684\u5173\u7cfb\u4e5f\u6bd4\u8f83\u590d\u6742\uff0c\u867d\u7136\u4f7f\u7528\u7f51\u7edc\u5bf9\u6570\u636e\u8fdb\u884c\u4e86\u5efa\u6a21\uff0c\u4f46\u662f\u5982\u679c\u4e0d\u80fd\u4ee5\u4e00\u79cd\u76f4\u89c2\u7684\u65b9\u5f0f\u5448\u73b0\u51fa\u6765\uff0c\u6211\u4eec\u4e5f\u5f88\u96be\u5feb\u901f\u628a\u63e1\u6570\u636e\u7684\u672c\u8d28\u3002\u590d\u6742\u7f51\u7edc\u7684\u53ef\u89c6\u5316\u5c06\u7f51\u7edc\u5448\u73b0\u5728\u4e8c\u7ef4\u6216\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u4e3a\u6211\u4eec\u5feb\u901f\u7406\u89e3\u4e00\u4e2a\u590d\u6742\u7f51\u7edc\u7684\u7ed3\u6784\u63d0\u4f9b\u4e86\u9ad8\u6548\u7684\u65b9\u6cd5\uff0c\u4e0e\u4e13\u4e1a\u7ecf\u9a8c\u76f8\u7ed3\u5408\u6709\u53ef\u80fd\u5f15\u51fa\u4e0e\u7814\u7a76\u95ee\u9898\u76f8\u5bf9\u66f4\u4e3a\u660e\u786e\u7684\u63a2\u7d22\u65b9\u5411\u3002\u7f51\u7edc\u53ef\u89c6\u5316\u53ef\u4ee5\u6839\u636e\u8282\u70b9\u7684\u51fa\u5ea6\u503c\u6216\u5165\u5ea6\u503c\u8bbe\u7f6e\u8282\u70b9\u7684\u5927\u5c0f\uff0c\u4ece\u800c\u4ece\u4e00\u4e2a\u4fa7\u9762\u53cd\u6620\u8282\u70b9\u7684\u91cd\u8981\u6027\u3002\u6211\u4eec\u9700\u8981\u6839\u636e\u7814\u7a76\u76ee\u7684\u4ee5\u53ca\u7f51\u7edc\u7ed3\u6784\u7684\u4e0d\u540c\uff0c\u9009\u62e9\u5408\u9002\u7684\u7f51\u7edc\u53ef\u89c6\u5316\u5e03\u5c40\uff0c\u4ece\u800c\u76f4\u89c2\u5730\u5448\u73b0\u7f51\u7edc\u7ed3\u6784\u3002\u6709\u5f88\u591a\u4e13\u95e8\u8fdb\u884c\u7f51\u7edc\u53ef\u89c6\u5316\u5e03\u5c40\u7684\u7b97\u6cd5\uff0c\u5176\u4e2d\u5c06\u8282\u70b9\u6a21\u62df\u4e3a\u7269\u7406\u7c92\u5b50\u4e4b\u95f4\u5f15\u529b\u5173\u7cfb\u7684\u529b\u5bfc\u5411\u56fe\uff08Force-Directed Graph\uff09\uff0c\u5982Kamada Kawai\u3001Fruchterman Reingold\u7b49\u7b97\u6cd5\uff0c\u5728\u68c0\u6d4b\u548c\u5448\u73b0\u7f51\u7edc\u4e2d\u7684\u793e\u56e2\uff08Community\uff09\u6bd4\u8f83\u6709\u6548\uff1bCircle Pack Layout[8]\u662f\u4e00\u79cd\u80fd\u591f\u8f83\u76f4\u89c2\u5730\u53cd\u6620\u8f83\u5927\u89c4\u6a21\u6570\u636e\u96c6\u5408\u5c42\u6b21\u5173\u7cfb\u7684\u7f51\u7edc\u5e03\u5c40\u5f62\u5f0f\uff0c\u5b83\u80fd\u591f\u5c06\u7f51\u7edc\u4e2d\u7684\u8282\u70b9\u805a\u7c7b\u3002\u6211\u4eec\u4e3b\u8981\u4f7f\u7528\u8fd9\u4e24\u79cd\u7f51\u7edc\u53ef\u89c6\u5316\u5e03\u5c40\uff0c\u9664\u6b64\u4e4b\u5916\u8fd8\u6709\u5f88\u591a\u4e0d\u540c\u7684\u53ef\u89c6\u5316\u5e03\u5c40\u7b97\u6cd5\uff0c\u8fd9\u91cc\u4e0d\u505a\u66f4\u591a\u4ecb\u7ecd\u3002<\/p>\n\n\n\n<p>\u7f51\u7edc\u53ef\u89c6\u5316\u53ef\u4ee5\u501f\u52a9\u4e13\u95e8\u7684\u7f51\u7edc\u53ef\u89c6\u5316\u5206\u6790\u8f6f\u4ef6\uff0c\u5982Gephi[9]\u3001Pajek[10]\u7b49\u5b9e\u73b0\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528Python\u3001R\u7b49\u901a\u7528\u7f16\u7a0b\u8bed\u8a00\u7684\u7f51\u7edc\u5206\u6790\u5305\u5b9e\u73b0\uff0c\u56fe1\u548c\u56fe2\u662f\u5728Gephi\u4e2d\u5206\u522b\u4f7f\u7528Fruchterman Reingold\u548cCircle Pack Layout\u5e03\u5c40\u5448\u73b0\u7684\u7ed3\u679c\u3002\u4e13\u95e8\u7684\u7f51\u7edc\u53ef\u89c6\u5316\u5206\u6790\u8f6f\u4ef6\u7684\u4f7f\u7528\u76f8\u5bf9\u6bd4\u8f83\u5bb9\u6613\uff0c\u4f46\u529f\u80fd\u76f8\u5bf9\u56fa\u5b9a\uff0c\u4e0d\u591f\u7075\u6d3b\uff1b\u7f16\u7a0b\u5b9e\u73b0\u7f51\u7edc\u5206\u6790\u548c\u53ef\u89c6\u5316\uff0c\u76f8\u5bf9\u6bd4\u8f83\u590d\u6742\uff0c\u4f46\u7075\u6d3b\u6027\u9ad8\u3002\u6211\u4eec\u5728\u8fdb\u884c\u300a\u6587\u6d77\u300b\u5b57\u5178\u7684\u7f51\u7edc\u6784\u5efa\u4e0e\u5206\u6790\u8fc7\u7a0b\u4e2d\uff0c\u8fd9\u4e24\u79cd\u65b9\u6cd5\u90fd\u6709\u6240\u5e94\u7528\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_6-3-1024x710.png\" alt=\"\" class=\"wp-image-20380\" width=\"600\" srcset=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_6-3-1024x710.png 1024w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_6-3-300x208.png 300w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_6-3-768x532.png 768w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_6-3-18x12.png 18w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_6-3.png 1134w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\">\u56fe2 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class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_7-2-1024x435.png\" alt=\"\" class=\"wp-image-20382\" width=\"600\" srcset=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_7-2-1024x435.png 1024w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_7-2-300x127.png 300w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_7-2-768x326.png 768w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_7-2-18x8.png 18w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_7-2.png 1364w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" 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class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_8-2-1024x581.png\" alt=\"\" class=\"wp-image-20383\" width=\"800\" srcset=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_8-2-1024x581.png 1024w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_8-2-300x170.png 300w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_8-2-768x436.png 768w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_8-2-18x10.png 18w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_8-2.png 1521w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\">\u56fe3 \u300a\u6587\u6d77\u300b\u4e2d\u7684\u5faa\u73af\u89e3\u91ca<\/p>\n\n\n\n<p class=\"has-text-align-center\">\uff08\u5de6\u53f3\u4e24\u56fe\u4e2d\u8282\u70b9\u7684\u5927\u5c0f\u53cd\u5e94\u8282\u70b9\u7684\u5ea6\u6570\uff09<\/p>\n\n\n\n<p>\u56fe3\u5c55\u793a\u7684\u300a\u6587\u6d77\u300b\u4e2d\u7684\u5faa\u73af\u89e3\u91ca\u6570\u91cf\u6bd4\u8f83\u591a\uff0c\u603b\u5171472\u4e2a\uff0c\u800c\u4e14\u6bd4\u8f83\u590d\u6742\uff0c\u5faa\u73af\u89e3\u91ca\u6709\u53ef\u80fd\u5171\u540c\u53c2\u4e0e\u67d0\u4e9b\u5b57\u610f\u4e49\u7684\u5f62\u6210\uff1b[15]\u5b57\u5178\u7f51\u7edc\u4e2d\u7684\u5f3a\u8fde\u63a5\u90e8\u4ef6\u867d\u7136\u4e5f\u6784\u6210\u5faa\u73af\uff0c\u4f46\u4e0d\u5b8c\u5168\u662f\u524d\u9762\u4ecb\u7ecd\u7684\u5faa\u73af\u89e3\u91ca\uff0c\u800c\u53ef\u80fd\u662f\u591a\u4e2a\u5355\u72ec\u7684\u5faa\u73af\u89e3\u91ca\u76f8\u4e92\u5173\u8054\u5f62\u6210\uff0c\u56e0\u6b64\u5f3a\u8fde\u63a5\u90e8\u4ef6\u5bf9\u4e8e\u63a2\u8ba8\u300a\u6587\u6d77\u300b\u6240\u4f53\u73b0\u897f\u590f\u5b57\u4e49\u5f62\u6210\u539f\u5219\u7684\u53ef\u80fd\u5177\u6709\u66f4\u5927\u7684\u4f5c\u7528\u3002<\/p>\n\n\n\n<p>\uff08\u4e8c\uff09\u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u4e2d\u7684\u5f3a\u8fde\u63a5\u90e8\u4ef6\u7684\u68c0\u6d4b<\/p>\n\n\n\n<p>\u5f3a\u8fde\u63a5\u90e8\u4ef6\uff08Strongly Connected Components, SCCs\uff09\u662f\u7f51\u7edc\u4e2d\u53ef\u4ee5\u76f8\u4e92\u5230\u8fbe\u7684\u5168\u90e8\u8282\u70b9\u7684\u96c6\u5408\uff0c\u4e00\u4e2a\u7f51\u7edc\u4e2d\u53ef\u80fd\u4f1a\u6709\u591a\u4e2a\u5f3a\u8fde\u63a5\u90e8\u4ef6\uff0c\u67e5\u627e\u7f51\u7edc\u4e2d\u7684\u5f3a\u8fde\u63a5\u90e8\u4ef6\u6709\u6bd4\u8f83\u6210\u719f\u7684\u7b97\u6cd5\u3002\u6211\u4eec\u5728\u67e5\u627e\u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u7684\u5f3a\u8fde\u63a5\u90e8\u4ef6\u65f6\u53ea\u9488\u5bf9\u300a\u6587\u6d77\u300b\u7684\u57fa\u672c\u5b57\u96c6\u5408\u6784\u6210\u7684\u7f51\u7edc\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_9-2-1024x346.png\" alt=\"\" class=\"wp-image-20384\" width=\"800\" srcset=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_9-2-1024x346.png 1024w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_9-2-300x101.png 300w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_9-2-768x260.png 768w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_9-2-18x6.png 18w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_9-2.png 1413w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\">\u88683 \u300a\u6587\u6d77\u300b\u57fa\u672c\u5b57\u7f51\u7edc\u5f3a\u8fde\u63a5\u90e8\u4ef6\uff08SCCs\uff09\u4e3e\u4f8b<\/p>\n\n\n\n<p>\u5728\u300a\u6587\u6d77\u300b1,389\u4e2a\u57fa\u672c\u5b57\u6784\u6210\u7684\u7f51\u7edc\u4e2d\uff0c\u5b58\u5728371\u4e2a\u5f3a\u8fde\u63a5\u90e8\u4ef6\uff0c\u5176\u4e2d\u6700\u5927\u7684\u5f3a\u8fde\u63a5\u90e8\u4ef6\u53ea\u6709\u4e00\u7ec4\uff0c\u5305\u62ec\u516d\u4e2a\u8282\u70b9\uff0c\u5373\u8fd9\u516d\u4e2a\u897f\u590f\u5b57\u5728\u89e3\u91ca\u5173\u7cfb\u65b9\u9762\u662f\u80fd\u591f\u4e92\u901a\u7684\uff0c\u5982\u88683\u6240\u793a\uff0c\u4ece\u5176\u4e2d\u6587\u91ca\u4e49\u6765\u770b\uff0c\u516d\u5b57SCC\u6784\u6210\u4e86\u4e00\u4e2a\u201c\u7537\u5b50\u3001\u5c0f\u5b69\u201d\u76f8\u5173\u7684\u8bed\u4e49\uff08\u540e\u9762\u4e24\u4e2a\u8868\u793a\u201c\u5b89\u9759\u3001\u5f90\u5f90\u201d\u7684\u897f\u590f\u5b57\u5728\u8bed\u4e49\u6784\u6210\u4e2d\u7684\u4f5c\u7528\u6211\u4eec\u7559\u5728\u540e\u7eed\u7684\u7814\u7a76\u4e2d\u89e3\u51b3\uff09\uff1b\u4e94\u5b57SCC\u4e5f\u53ea\u6709\u4e00\u7ec4\uff0c\u8fd9\u4e9b\u5b57\u6784\u6210\u4e86\u201c\u62bd\u3001\u62d4\u201d\u52a8\u4f5c\u76f8\u5173\u7684\u8bed\u4e49\uff1b\u56db\u5b57SCC\u5171\u670917\u7ec4\uff0c\u8868\u4e2d\u7ed9\u51fa\u7684\u56db\u5b57SCC\u6784\u6210\u4e86\u201c\u80dc\u3001\u5f3a\u201d\u76f8\u5173\u7684\u8bed\u4e49\u3002<\/p>\n\n\n\n<p>\uff08\u4e09\uff09\u300a\u6587\u6d77\u300b\u4e2d\u897f\u590f\u5b57\u89e3\u91ca\u5c42\u6b21\u7ed3\u6784\u7684\u6784\u5efa<\/p>\n\n\n\n<p>\u300a\u6587\u6d77\u300b\u57fa\u672c\u5b57\u96c6\u80fd\u591f\u5b9a\u4e49\u6240\u6709\u5176\u4f59\u7684\u5b57\uff0c\u6211\u4eec\u901a\u8fc7\u8ba1\u7b97\u300a\u6587\u6d77\u300b\u4e2d\u6bcf\u4e2a\u5b57\u8ddd\u79bb\u57fa\u672c\u5b57\u96c6\u7684\u5b9a\u4e49\u8def\u5f84\u957f\u5ea6\uff0c\u6765\u786e\u5b9a\u300a\u6587\u6d77\u300b\u4e2d\u897f\u590f\u5b57\u7684\u89e3\u91ca\u5c42\u6b21\u7ed3\u6784\u3002\u6211\u4eec\u9996\u5148\u63d0\u51fa\u4e00\u4e2a\u6982\u5ff5\uff1a\u5b9a\u4e49\u8ddd\u79bb\uff0c\u8bb0\u4e3a<em>dis(w)<\/em>\uff0c\u5176\u4e2d<em>w<\/em>\u8868\u793a\u300a\u6587\u6d77\u300b\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u897f\u590f\u5b57\uff0c\u5b9a\u4e49\u8ddd\u79bb\u8868\u793a\u4e3a\uff1a\u300a\u6587\u6d77\u300b\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u5b57\u4ee5\u57fa\u672c\u5b57\u96c6\u4e2d\u7684\u67d0\u4e2a\u5b57\u4e3a\u8d77\u70b9\uff0c\u901a\u8fc7\u5b57\u5178\u4e2d\u8bcd\u6761\u7684\u5b9a\u4e49\uff0c\u5230\u8fbe\u8be5\u897f\u590f\u5b57\u9700\u8981\u7ecf\u8fc7\u7684\u63a8\u5bfc\u6b21\u6570\uff08\u5373\u7f51\u7edc\u4e2d\uff0c\u4ece\u57fa\u672c\u5b57\u96c6\u5408\u4e2d\u7684\u67d0\u5b57\u5230\u8be5\u5b57\u7684\u8def\u5f84\u957f\u5ea6\uff09\u3002\u8fd9\u6837\uff0c\u5982\u679c\u8be5\u5b57\u5305\u542b\u5728\u57fa\u672c\u5b57\u96c6\u4e2d\uff0c\u5219<em>dis(w)=<\/em>0\uff1b\u5982\u679c\u662f\u4ece\u57fa\u672c\u5b57\u7ecf\u8fc7\u4e00\u6b65\u5c31\u53ef\u4ee5\u5c06<em>w<\/em>\u63a8\u5bfc\u51fa\u6765\uff0c\u5373\u8be5\u5b57\u7684\u6240\u6709\u201c\u6784\u5b57\u201d\u90fd\u5728\u57fa\u672c\u5b57\u96c6\u4e2d\uff0c\u5219<em>dis(w)=<\/em>1\uff0c\u5426\u5219<em>dis(w)=<\/em>max{<em>dis(v)<\/em>}+1\uff0c\u5176\u4e2d<em>v<\/em>\u8868\u793a\u51fa\u73b0\u5728<em>w<\/em>\u7684\u89e3\u91ca\u4e2d\u7684\u6240\u6709\u5b57\uff08\u300a\u6587\u6d77\u300b\u4e2d\u4e3a\u4e24\u4e2a\u201c\u6784\u5b57\u201d\uff09\u3002\u7531\u6b64\u53ef\u89c1\u8be5\u5b9a\u4e49\u8ddd\u79bb\u662f\u4e00\u4e2a\u9012\u5f52\u5b9a\u4e49\u3002<\/p>\n\n\n\n<p>\u7531\u4e0a\u8ff0\u5b9a\u4e49\u8ddd\u79bb\u539f\u5219\u6784\u5efa\u7684\u300a\u6587\u6d77\u300b\u897f\u590f\u5b57\u89e3\u91ca\u5c42\u6b21\u7ed3\u6784\u5982\u56fe4\u6240\u793a\uff0c\u56fe\u4e2d\u8868\u793a\u4e86\u4e09\u4e2a\u5c42\u6b21\u7ed3\u6784\u7684\u793a\u4f8b\uff1a\uff081\uff09\u4e2d\u5fc3\u9ec4\u8272\u533a\u57df\u8868\u793a\u5b57\u5178\u7f51\u7edc\u7684\u57fa\u672c\u5b57\u96c6\uff0c\u5305\u542b\u82e5\u5e72\u5f3a\u8fde\u63a5\u90e8\u4ef6\uff0c\u5176\u4e2d\u7684\u897f\u590f\u5b57\uff08\u7a7a\u767d\u5706\u5708\uff09\u7684\u5b9a\u4e49\u8ddd\u79bb<em>dis(w)<\/em>\u7686\u4e3a0\uff1b\uff082\uff09\u6d45\u84dd\u8272\u533a\u57df\u4e2d\u7684\u897f\u590f\u5b57\uff08\u84dd\u8272\u5706\u70b9\uff09\u7684\u5b9a\u4e49\u8ddd\u79bb<em>dis(w)<\/em>\u7686\u4e3a1\uff1b\uff083\uff09\u6d45\u7eff\u8272\u533a\u57df\u4e2d\u7684\u897f\u590f\u5b57\uff08\u7eff\u8272\u5706\u70b9\uff09\u7684\u5b9a\u4e49\u8ddd\u79bb<em>dis(w)<\/em>\u7686\u4e3a2\u3002\u6ce8\u610f\u7eff\u8272\u5706\u70b9\u4ee3\u8868\u7684\u5904\u5728\u7b2c\u4e09\u5c42\u6b21\u7684\u897f\u590f\u5b57\u7684\u201c\u6784\u5b57\u201d\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u662f\u6765\u81ea\u7b2c\u4e8c\u5c42\u6b21\uff08\u84dd\u8272\u5706\u70b9\u8868\u793a\uff09\uff0c\u4e5f\u53ef\u80fd\u6709\u6765\u81ea\u57fa\u672c\u5b57\u96c6\u7684\u201c\u6784\u5b57\u201d\uff0c\u5982\u56fe\u4e2d\u6807\u51fa\u76841\u30012\u30013\u6761\u89e3\u91ca\u8fb9\u6240\u793a\uff0c\u7531\u6b64\u53ef\u89c1\uff1a\u4e00\u4e2a\u5b57\u6240\u5904\u7684\u5c42\u6b21\u662f\u6839\u636e\u5176\u6240\u6709\u201c\u6784\u5b57\u201d\u4e2d\u6240\u5904\u7684\u6700\u5927\u7684\u5c42\u6b21+1\u5f97\u5230\u3002\u6211\u4eec\u8ba1\u7b97\u300a\u6587\u6d77\u300b\u4e2d\u6bcf\u4e2a\u5b57\u7684\u5b9a\u4e49\u8ddd\u79bb\uff0c\u5728\u57fa\u672c\u5b57\u96c6\u4ee5\u5916\uff0c\u6bcf\u4e00\u5c42\u6b21\u7684\u897f\u590f\u5b57\u7684\u6570\u91cf\u5982\u88684\u6240\u793a\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_10-2.png\" alt=\"\" class=\"wp-image-20385\" width=\"600\" srcset=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_10-2.png 801w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_10-2-300x297.png 300w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_10-2-768x759.png 768w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_10-2-12x12.png 12w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_10-2-100x100.png 100w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_10-2-45x45.png 45w\" sizes=\"(max-width: 801px) 100vw, 801px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\">\u56fe4 \u300a\u6587\u6d77\u300b\u5b57\u5178\u89e3\u91ca\u5c42\u6b21\u7ed3\u6784\u793a\u610f\u56fe<\/p>\n\n\n\n<p>\u901a\u8fc7\u88684\u7684\u6570\u636e\u6211\u4eec\u53ef\u4ee5\u770b\u51fa\uff0c\u6574\u4e2a\u300a\u6587\u6d77\u300b\u7684\u897f\u590f\u5b57\u6839\u636e\u5b9a\u4e49\u8ddd\u79bb\u53ef\u4ee5\u5206\u4e3a6\u4e2a\u5c42\u6b21\uff1a\u7b2c0\u5c42\u4e3a\u57fa\u672c\u5b57\u51711,389\u4e2a\u5b57\uff0c\u7b2c1\u20145\u5c42\u51711,581\u4e2a\u5b57\uff0c\u5408\u8ba12,970\u4e2a\u5b57\uff0c\u5bf9\u5e94\u56fe1\u4e2d\u7eff\u8272\u533a\u57df\u8986\u76d6\u7684\u8282\u70b9\u603b\u6570\u3002\u4ece\u5f97\u5230\u7684\u897f\u590f\u5b57\u89e3\u91ca\u7f51\u7edc\u7684\u5c42\u6b21\u7ed3\u6784\u6765\u770b\uff0c\u591a\u6570\u897f\u590f\u5b57\u96c6\u4e2d\u5728\u57fa\u672c\u5b57\u96c6\u548c\u7b2c\u4e00\u3001\u4e8c\u5c42\u6b21\uff0c\u8ddd\u79bb\u57fa\u672c\u5b57\u96c6\u8f83\u8fdc\u7684\u5c42\u6b21\u4e0a\u7684\u5b57\u6570\u76f8\u5bf9\u6bd4\u8f83\u5c11\u3002\u867d\u7136\u672c\u6587\u5206\u6790\u7684\u6570\u636e\u662f\u300a\u6587\u6d77\u300b\u4e2d\u897f\u590f\u5b57\u7684\u4e00\u90e8\u5206\uff0c\u4f46\u8fd9\u90e8\u5206\u5b57\u89e3\u91ca\u5173\u7cfb\u5b8c\u6574\uff0c\u80fd\u591f\u4f53\u73b0\u300a\u6587\u6d77\u300b\u4e2d\u897f\u590f\u5b57\u89e3\u91ca\u7684\u7279\u70b9\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_11-2-1024x672.png\" alt=\"\" class=\"wp-image-20386\" width=\"600\" srcset=\"https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_11-2-1024x672.png 1024w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_11-2-300x197.png 300w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_11-2-768x504.png 768w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_11-2-18x12.png 18w, https:\/\/achieve.dhcn.cn\/wp-content\/uploads\/2023\/06\/Tu_11-2.png 1136w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\">\u88684 \u4e0d\u540c\u5b9a\u4e49\u5c42\u6b21\u7684\u897f\u590f\u5b57\u6570\u91cf<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>\u7ed3<\/strong><strong> <\/strong><strong>\u8bed<\/strong><strong><\/strong><\/p>\n\n\n\n<p>\u7f51\u7edc\u5206\u6790\uff0c\u7279\u522b\u662f\u793e\u4f1a\u7f51\u7edc\u5206\u6790\uff0c\u5728\u6570\u5b57\u4eba\u6587\u9886\u57df\u5df2\u7ecf\u5f00\u59cb\u53d1\u6325\u91cd\u8981\u7684\u4f5c\u7528\uff0c\u4eba\u6587\u5b66\u8005\u5bf9\u4e8e\u7f51\u7edc\u5206\u6790\u65b9\u6cd5\u7684\u5e94\u7528\u4e5f\u8d8a\u6765\u8d8a\u91cd\u89c6\u3002\u672c\u6587\u4ee5\u897f\u590f\u6587\u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u7684\u6784\u5efa\u4e0e\u5e94\u7528\u4e3a\u4f8b\u8ba8\u8bba\u4e86\u57fa\u4e8e\u7f51\u7edc\u5206\u6790\u6280\u672f\u7684\u5faa\u73af\u89e3\u91ca\u7ed3\u6784\u4ee5\u53ca\u5f3a\u8fde\u63a5\u90e8\u4ef6\u7684\u68c0\u6d4b\u65b9\u6cd5\uff0c\u4ee5\u300a\u6587\u6d77\u300b\u5b57\u5178\u7684\u5b57\u578b\u89e3\u91ca\u5173\u7cfb\u6784\u5efa\u897f\u590f\u57fa\u672c\u5b57\u96c6\u7684\u65b9\u6cd5\uff0c\u4ee5\u53ca\u6839\u636e\u300a\u6587\u6d77\u300b\u89e3\u91ca\u4e2d\u897f\u590f\u5b57\u4e0e\u57fa\u672c\u5b57\u4e4b\u95f4\u7684\u5b9a\u4e49\u8ddd\u79bb\u6784\u5efa\u300a\u6587\u6d77\u300b\u897f\u590f\u5b57\u89e3\u91ca\u7684\u5c42\u6b21\u7ed3\u6784\u7684\u65b9\u6cd5\u3002\u672c\u7814\u7a76\u5e0c\u671b\u80fd\u591f\u4e3a\u73b0\u4ee3\u4eba\u5b66\u4e60\u548c\u7814\u7a76\u897f\u590f\u6587\u63d0\u4f9b\u4e00\u79cd\u4f18\u5316\u65b9\u6848\uff0c\u80fd\u591f\u4e3a\u8fd8\u539f\u300a\u6587\u6d77\u300b\u7684\u7f16\u64b0\u601d\u8def\u63d0\u4f9b\u4e00\u79cd\u6280\u672f\u624b\u6bb5\u7684\u652f\u6301\u3002<\/p>\n\n\n\n<p>\u300a\u6587\u6d77\u300b\u4e2d\u7684\u5b57\u578b\u89e3\u91ca\u5173\u7cfb\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u80fd\u591f\u53cd\u6620\u5f53\u65f6\u7684\u4eba\u4eec\u5728\u5b66\u4e60\u897f\u590f\u6587\u65f6\u6240\u9075\u5faa\u7684\u5927\u81f4\u987a\u5e8f\uff0c\u4f46\u662f\u8fd9\u4e0e\u5f53\u65f6\u5b9e\u9645\u751f\u6d3b\u4e2d\u7684\u5e94\u7528\u53ef\u80fd\u5b58\u5728\u533a\u522b\uff0c\u800c\u8fd9\u4e9b\u53ef\u80fd\u4ece\u897f\u590f\u6587\u5386\u53f2\u6587\u732e\u7684\u7528\u5b57\u65b9\u9762\u6709\u6240\u4f53\u73b0\uff0c\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u501f\u52a9\u73b0\u4ee3\u4eba\u5de5\u667a\u80fd\u65b9\u6cd5\u5c06\u897f\u590f\u6587\u4e16\u4fd7\u6587\u732e\u8fdb\u884c\u5206\u6790\uff0c\u4e0e\u300a\u6587\u6d77\u300b\u5b57\u5178\u7f51\u7edc\u7684\u7814\u7a76\u7ed3\u8bba\u4e92\u76f8\u5370\u8bc1\u548c\u8865\u5145\uff0c\u5c06\u80fd\u591f\u66f4\u52a0\u51c6\u786e\u5730\u53cd\u6620\u897f\u590f\u5b57\u8bed\u4e49\u7684\u5f62\u6210\u4e0e\u884d\u751f\u8fc7\u7a0b\uff0c\u4e5f\u6709\u53ef\u80fd\u4e3a\u57fa\u4e8e\u4fe1\u606f\u6280\u672f\u7684\u4e2d\u56fd\u5176\u4ed6\u53e4\u6587\u5b57\u7684\u7814\u7a76\u63d0\u4f9b\u53c2\u8003\u3002<\/p>\n\n\n\n<p>Network Analysis of the Tangut Dictionary <strong><em>Wenhai<\/em><\/strong><\/p>\n\n\n\n<p>Zhang Guangwei<\/p>\n\n\n\n<p><strong>Abstract:<\/strong> Social network analysis has become an important data visualization and analysis method in digital humanities. This paper constructed a definition model of Tangut characters in the Tangut dictionary <em>Wenhai<\/em> by converting it into a dictionary network. Tangut scholars have done a lot of research on Tangut character patterns using manual analysis methods. However, it is not easy to form a widely accepted interpretation due to the massive number of Tangut characters and the complex definition relationships. The dictionary network constructed based on <em>Wenhai<\/em> written by the Tangut people can help us gain insight into the glyph characteristics and the origin of the meaning of the Tangut characters. We showed the definition structure of <em>Wenhai<\/em> with the visualization of the dictionary network. We proposed a method for constructing the core set of the Tangut characters based on the reachability of nodes in the dictionary network. We detected the loops and strong connected components in the <em>Wenhai<\/em> dictionary network and analyzed their roles in the meaning formation of Tangut characters. We constructed the definition hierarchies in <em>Wenhai<\/em> based on the definition distance from the core set to the Tangut characters. We hope to provide an optimized solution for modern people to study Tangut characters and a technical means to support the restoration of <em>Wenhai<\/em>. This method might be helpful for the study of ancient Chinese characters based on information technology.<\/p>\n\n\n\n<p><strong>Keywords:<\/strong> Tangut Dictionary; <em>Wenhai<\/em>; Network Analysis; Definition Loop; Definition Distance; Definition Hierarchies<\/p>\n\n\n\n<p class=\"has-text-align-right\">\uff08\u7f16\u8f91\uff1a\u8bb8\u53ef\uff09<\/p>\n\n\n\n<p>\u6ce8\u91ca\uff1a<\/p>\n\n\n\n<p>*\u672c\u6587\u662f\u6559\u80b2\u90e8\u4eba\u6587\u793e\u4f1a\u79d1\u5b66\u7814\u7a76\u9752\u5e74\u57fa\u91d1\u9879\u76ee\u201c\u57fa\u4e8e\u6df1\u5ea6\u5b66\u4e60\u7684\u897f\u590f\u6587\u81ea\u52a8\u8bc6\u522b\u7cfb\u7edf\u201d(17YJCZH239)\u7684\u9636\u6bb5\u6027\u7814\u7a76\u6210\u679c\u3002<\/p>\n\n\n\n<p>[1]\u6851\u660e\u5ce9\uff1a\u300a\u6211\u56fd\u897f\u590f\u6587\u8f9e\u4e66\u3008\u6587\u6d77\u3009\u53ca\u5176\u4ed6\u300b\uff0c\u300a\u8f9e\u4e66\u7814\u7a76\u300b1980\u5e74\u7b2c1\u671f\u3002<\/p>\n\n\n\n<p>[2]\u53f2\u91d1\u6ce2\uff1a\u300a\u65b0\u89c1\u897f\u590f\u6587\u504f\u65c1\u90e8\u9996\u548c\u8349\u4e66\u523b\u672c\u6587\u732e\u8003\u91ca\u300b\uff0c\u300a\u6c11\u65cf\u8bed\u6587\u300b2017\u5e74\u7b2c2\u671f\u3002<\/p>\n\n\n\n<p>[3]\u9f9a\u714c\u57ce\uff1a\u300a\u897f\u590f\u6587\u5b57\u884d\u751f\u8fc7\u7a0b\u7684\u91cd\u5efa\u300b\uff0c\u300a\u201c\u56fd\u7acb\u201d\u653f\u6cbb\u5927\u5b66\u8fb9\u653f\u7814\u7a76\u6240\u5e74\u62a5\u300b1984\u5e74\u7b2c15\u671f\u3002<\/p>\n\n\n\n<p>[4]\u897f\u7530\u9f99\u96c4\u3001\u9c81\u5fe0\u6167\uff1a\u300a\u897f\u590f\u6587\u5b57\u7684\u5206\u6790\u300b\uff0c\u300a\u897f\u590f\u7814\u7a76\u300b2012\u5e74\u7b2c2\u671f\u3002<\/p>\n\n\n\n<p>[5]\u97e9\u5c0f\u5fd9\uff1a\u300a\u897f\u590f\u6587\u7684\u9020\u5b57\u6a21\u5f0f\u300b\uff0c\u5317\u4eac\uff1a\u4e2d\u56fd\u793e\u4f1a\u79d1\u5b66\u51fa\u7248\u793e\uff0c2016\u5e74\uff0c\u7b2c13\u201499\u9875\u3002<\/p>\n\n\n\n<p>[6]\u97e9\u5c0f\u5fd9\uff1a\u300a\u897f\u590f\u6587\u7684\u9020\u5b57\u6a21\u5f0f\u300b\uff0c\u7b2c7\u9875\u3002<\/p>\n\n\n\n<p>[7]Philippe Vincent-Lamarre et al., &#8220;The Latent Structure of Dictionaries,&#8221; <em>Topics in Cognitive Science<\/em>, vol. 8, no. 3, 2016, pp. 625-659.<\/p>\n\n\n\n<p>[8]Weixin Wang et al., \u201cVisualization of Large Hierarchical Data by Circle Packing,\u201d Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, 2006, pp. 517-520.<\/p>\n\n\n\n<p>[9]Gephi-The Open Graph Viz Platform, https:\/\/gephi.org\/.<\/p>\n\n\n\n<p>[10]Andrej Mrvar, Vladimir Batagelj, \u201cAnalysis and Visualization of Large Networks with Program Package Pajek,\u201d <em>Complex Adaptive Systems Modeling<\/em>, vol. 4, no. 1, 2016, pp. 1-8.<\/p>\n\n\n\n<p>[11]Camilo Garrido, Claudio Gutierrez, \u201cDictionaries as Networks: Identifying the Graph Structure of Ogden&#8217;s Basic English,\u201d Proceedings of COLING 2016, the 26th International Conference on Computational Linguistics: Technical Papers, 2016, pp. 3565-3576; COGNITIVE 2018: The Tenth International Conference on Advanced Cognitive Technologies and Applications, 2018, Barcelona, Spain, pp. 18-23.<\/p>\n\n\n\n<p>[12]Olivier Picard et al., &#8220;Hierarchies in Dictionary Definition Space,&#8221; arXiv:0911.5703 [cs], 2009.<\/p>\n\n\n\n<p>[13]David Levary et al., \u201cLoops and Self-Reference in the Construction of Dictionaries,\u201d <em>Physical Review X<\/em>, vol. 2, no. 3, 2012, DOI:10.1103\/PhysRevX.2.031018.<\/p>\n\n\n\n<p>[14]\u97e9\u5c0f\u5fd9\uff1a\u300a\u897f\u590f\u6587\u7684\u9020\u5b57\u6a21\u5f0f\u300b\uff0c\u7b2c17\u9875\u3002<\/p>\n\n\n\n<p>[15]David Levary et al., \u201cLoops and Self-Reference in the Construction of Dictionaries,\u201d 2012.<\/p>","protected":false},"excerpt":{"rendered":"<p>\u5f20\u5149\u4f1f \/ \u9655\u897f\u5e08\u8303\u5927\u5b66\u5386\u53f2\u6587\u5316\u5b66\u9662 \u6458 \u8981\uff1a\u793e\u4f1a\u7f51\u7edc\u5206\u6790\u5df2\u7ecf\u6210\u4e3a\u6570\u5b57\u4eba\u6587\u9886\u57df\u91cd\u8981\u7684\u6570\u636e\u53ef\u89c6\u5316\u4e0e\u5206\u6790\u7684\u65b9\u6cd5\uff0c\u6587 [&hellip;]<\/p>","protected":false},"author":3,"featured_media":20380,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[4956],"tags":[4959,4961,4960,29,347,4958,4962],"class_list":["post-20374","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-4956","tag-4959","tag-4961","tag-4960","tag-29","tag-347","tag-4958","tag-4962"],"blocksy_meta":{"styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":6}},"_links":{"self":[{"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/posts\/20374","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/comments?post=20374"}],"version-history":[{"count":1,"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/posts\/20374\/revisions"}],"predecessor-version":[{"id":20387,"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/posts\/20374\/revisions\/20387"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/media\/20380"}],"wp:attachment":[{"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/media?parent=20374"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/categories?post=20374"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/achieve.dhcn.cn\/en\/wp-json\/wp\/v2\/tags?post=20374"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}