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第9行： − ==历史== − + − ==测量== − − − 一张图的三元闭合的两个最常见的度量是（不按特定顺序）该图的'''<font color="#FF8000">聚类系数 Clustering Coefficient </font>'''和'''<font color="#FF8000">可传递性 Transitivity </font>'''。+ + − + 第35行：
第32行： − 衡量三元闭包的一种方法是聚类系数，如下所示：+ 第43行：
第40行： − +
无编辑摘要
==History==
==History==
Triadic closure was made popular by [[Mark Granovetter]] in his 1973 article ''The Strength of Weak Ties''.<ref>Granovetter, M. (1973). "[http://www.stanford.edu/dept/soc/people/mgranovetter/documents/granstrengthweakties.pdf The Strength of Weak Ties] {{webarchive|url=https://web.archive.org/web/20080216103216/http://www.stanford.edu/dept/soc/people/mgranovetter/documents/granstrengthweakties.pdf |date=2008-02-16 }}", American Journal of Sociology, Vol. 78, Issue 6, May 1360-80.</ref> There he synthesized the theory of [[cognitive balance]] first introduced by [[Fritz Heider]] in 1946 with a Simmelian understanding of social networks. In general terms, cognitive balance refers to the propensity of two individuals to want to feel the same way about an object. If the triad of three individuals is not closed, then the person connected to both of the individuals will want to close this triad in order to achieve closure in the relationship network.
Triadic closure was made popular by [[Mark Granovetter]] in his 1973 article ''The Strength of Weak Ties''.<ref>Granovetter, M. (1973). "[http://www.stanford.edu/dept/soc/people/mgranovetter/documents/granstrengthweakties.pdf The Strength of Weak Ties] {{webarchive|url=https://web.archive.org/web/20080216103216/http://www.stanford.edu/dept/soc/people/mgranovetter/documents/granstrengthweakties.pdf |date=2008-02-16 }}", American Journal of Sociology, Vol. 78, Issue 6, May 1360-80.</ref> There he synthesized the theory of [[cognitive balance]] first introduced by [[Fritz Heider]] in 1946 with a Simmelian understanding of social networks. In general terms, cognitive balance refers to the propensity of two individuals to want to feel the same way about an object. If the triad of three individuals is not closed, then the person connected to both of the individuals will want to close this triad in order to achieve closure in the relationship network.
Triadic closure was made popular by Mark Granovetter in his 1973 article The Strength of Weak Ties. There he synthesized the theory of cognitive balance first introduced by Fritz Heider in 1946 with a Simmelian understanding of social networks. In general terms, cognitive balance refers to the propensity of two individuals to want to feel the same way about an object. If the triad of three individuals is not closed, then the person connected to both of the individuals will want to close this triad in order to achieve closure in the relationship network.
Triadic closure was made popular by Mark Granovetter in his 1973 article The Strength of Weak Ties. There he synthesized the theory of cognitive balance first introduced by Fritz Heider in 1946 with a Simmelian understanding of social networks. In general terms, cognitive balance refers to the propensity of two individuals to want to feel the same way about an object. If the triad of three individuals is not closed, then the person connected to both of the individuals will want to close this triad in order to achieve closure in the relationship network.
==历史==
马克·格兰诺维特 Mark Granovetter在1973年发表的《弱链接的力量》 The Strength of Weak Ties一文使得三元闭包性质变得流行。 在那里，他综合了弗里茨·海德 Fritz Heider于1946年提出的'''<font color="#FF8000">认知平衡理论 The Theory Of Cognitive Balance </font>'''以及Georg Simmel对社会网络的理解。 一般而言，认知平衡是指两个个体对同一事物具有产生相同感觉的倾向。 如果三个个体所组成的三元组没有闭合，那么与同一个体联系的其余两个个体均将想要闭合这一三元组，进而在关系网络中形成闭包。
马克·格兰诺维特 Mark Granovetter在1973年发表的《弱链接的力量》 The Strength of Weak Ties一文使得三元闭包性质变得流行。 在那里，他综合了弗里茨·海德 Fritz Heider于1946年提出的'''<font color="#FF8000">认知平衡理论 The Theory Of Cognitive Balance </font>'''以及Georg Simmel对社会网络的理解。 一般而言，认知平衡是指两个个体对同一事物具有产生相同感觉的倾向。 如果三个个体所组成的三元组没有闭合，那么与同一个体联系的其余两个个体均将想要闭合这一三元组，进而在关系网络中形成闭包。
==Measurements==
==Measurements==
{{Unreferenced section|date=September 2009}}
{{Unreferenced section|date=September 2009}}
The two most common measures of triadic closure for a graph are (in no particular order) the [[clustering coefficient]] and transitivity for that graph.
The two most common measures of triadic closure for a graph are (in no particular order) the [[clustering coefficient]] and transitivity for that graph.
The two most common measures of triadic closure for a graph are (in no particular order) the clustering coefficient and transitivity for that graph.
The two most common measures of triadic closure for a graph are (in no particular order) the clustering coefficient and transitivity for that graph.
==测量==
最常见的两种测度一张图三元闭包性质的两种方法（排名不分先后）是采用该图的'''<font color="#FF8000">聚集系数 Clustering Coefficient </font>'''和'''<font color="#FF8000">传递性 Transitivity </font>'''。
==Clustering coefficient==
==Clustering coefficient==
聚类系数<br>
==聚类系数==
One measure for the presence of triadic closure is [[clustering coefficient]], as follows:
One measure for the presence of triadic closure is [[clustering coefficient]], as follows:
One measure for the presence of triadic closure is clustering coefficient, as follows:
One measure for the presence of triadic closure is clustering coefficient, as follows:
测度三元闭包是否出现的方法之一是聚集系数，如下所示：
Let <math>G = (V,E)</math> be an undirected simple graph (i.e., a graph having no self-loops or multiple edges) with V the set of vertices and E the set of edges. Also, let <math>N = |V|</math> and <math>M = |E|</math> denote the number of vertices and edges in G, respectively, and let <math>d_i</math> be the degree of vertex i.
Let <math>G = (V,E)</math> be an undirected simple graph (i.e., a graph having no self-loops or multiple edges) with V the set of vertices and E the set of edges. Also, let <math>N = |V|</math> and <math>M = |E|</math> denote the number of vertices and edges in G, respectively, and let <math>d_i</math> be the degree of vertex i.
令<math>G =（V，E）</math>是无向的'''<font color="#FF8000">简单图 Simple Graph </font>'''（即没有自环或多个边的图），其中V为顶点集，E为边集。 另外，令<math>N = |V|</math>和<math>M = |E|</math>分别表示G中顶点和边的数量，并令<math>d_i</math> 是顶点的度i。
令<math>G =(V，E)</math>是无向简单图（即，没有自环或多重边的图），其中<math>V</math>为节点集，<math>E</math>为边集。 另外，令<math>N = |V|</math>和<math>M = |E|</math>分别表示图<math>G</math>中节点和边的数量，并令<math>d_i</math> 是节点<math>i</math>的度。