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| 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. |
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− | 令<math>G =(V,E)</math>是无向的简单图(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。 |
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| Now, for a vertex <math>i</math> with <math>d_i \ge 2</math>, the clustering coefficient <math>c(i)</math> of vertex <math>i</math> is the fraction of triples for vertex <math>i</math> that are closed, and can be measured as <math>\frac{\delta (i)}{\tau (i)}</math>. Thus, the clustering coefficient <math>C(G)</math> of graph <math>G</math> is given by <math>C(G) = \frac {1}{N_2} \sum_{i \in V, d_i \ge 2} c(i)</math>, where <math>N_2</math> is the number of nodes with degree at least 2. | | Now, for a vertex <math>i</math> with <math>d_i \ge 2</math>, the clustering coefficient <math>c(i)</math> of vertex <math>i</math> is the fraction of triples for vertex <math>i</math> that are closed, and can be measured as <math>\frac{\delta (i)}{\tau (i)}</math>. Thus, the clustering coefficient <math>C(G)</math> of graph <math>G</math> is given by <math>C(G) = \frac {1}{N_2} \sum_{i \in V, d_i \ge 2} c(i)</math>, where <math>N_2</math> is the number of nodes with degree at least 2. |
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− | 现在,对于具有<math> d_i \ ge 2 </ math>的顶点<math> i </ math>,顶点<math> i </ math>的聚类系数<math> c(i)</ math> 是封闭的顶点<math> i </ math>的三元组分数,可以测量为<math> \ frac {\ delta(i)} {\ tau(i)} </ math>。 因此,图<math> G </ math>的聚类系数<math> C(G)</ math>由<math> C(G)= \ frac {1} {N_2} \ sum_ {i \ 在V中,d_i \ ge 2} c(i)</ math>,其中<math> N_2 </ math>是度数至少为2的节点数。 | + | 现在,对于具有<math>d_i\ge 2</math>的顶点<math>i</ math>,顶点<math>i</math>的聚类系数<math>c(i)</math> 是封闭的顶点<math>i</math>的三元组分数,可以测量为<math>\frac{\delta(i)}{\tau(i)}</math>。 因此,图<math> G </math>的聚类系数<math> C(G)</math>由<math> C(G)=\frac {1}{N_2} \sum_{i \in V,d_i \ge 2}c(i)</math>,其中<math>N_2</math>是度数至少为2的节点数。 |
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− | ===Transitivity===
| + | ==Transitivity== |
| + | 传递性<br> |
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| Another measure for the presence of triadic closure is transitivity, defined as <math>T(G) = \frac{3\delta (G)}{\tau (G)}</math>. | | Another measure for the presence of triadic closure is transitivity, defined as <math>T(G) = \frac{3\delta (G)}{\tau (G)}</math>. |
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| Another measure for the presence of triadic closure is transitivity, defined as <math>T(G) = \frac{3\delta (G)}{\tau (G)}</math>. | | Another measure for the presence of triadic closure is transitivity, defined as <math>T(G) = \frac{3\delta (G)}{\tau (G)}</math>. |
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− | 存在三元闭包的另一个度量是传递性,定义为 < math > t (g) = frac {3 delta (g)}{ tau (g)} </math > 。
| + | 关于三元闭包的另一种度量是可传递性,定义为<math>T(G)= \frac{3\delta(G)}{\tau(G)}</math>。 |
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| ==Causes and effects== | | ==Causes and effects== |