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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.

令<math>G =(V，E)</math>是'''<font color="#FF8000">无向简单图 Undirected Simple Graph</font>'''（即，没有'''<font color="#FF8000">自环 Self-loops</font>'''或'''<font color="#FF8000">多重边 Multiple Edges</font>'''的图），其中<math>V</math>为'''<font color="#FF8000">顶点 Vertice</font>'''集，<math>E</math>为'''<font color="#FF8000">边 Edge</font>'''集。 另外，令<math>N = |V|</math>和<math>M = |E|</math>分别表示'''<font color="#FF8000">图</font>'''<math>G</math>中'''<font color="#FF8000">顶点</font>'''和'''<font color="#FF8000">边</font>'''的数量，并令<math>d_i</math> 表示'''<font color="#FF8000">顶点</font>'''<math>i</math>的'''<font color="#FF8000">度 Degree</font>'''。

令<math>G =(V，E)</math>是'''<font color="#FF8000">无向简单图 Undirected Simple Graph</font>'''（即，没有'''<font color="#FF8000">自环 Self-loops</font>'''或'''<font color="#FF8000">多重边 Multiple Edges</font>'''的图），其中<math>V</math>为'''<font color="#FF8000">顶点 Vertice</font>'''集，<math>E</math>为'''<font color="#FF8000">边 Edge</font>'''集。 另外，令<math>N = |V|</math>和<math>M = |E|</math>分别表示图<math>G</math>中顶点和边的数量，并令<math>d_i</math> 表示顶点<math>i</math>的'''<font color="#FF8000">度 Degree</font>'''。

We can define a triangle among the triple of vertices <math>i</math>, <math>j</math>, and <math>k</math> to be a set with the following three edges: {(i,j), (j,k), (i,k)}.  

We can define a triangle among the triple of vertices <math>i</math>, <math>j</math>, and <math>k</math> to be a set with the following three edges: {(i,j), (j,k), (i,k)}.  

We can define a triangle among the triple of vertices <math>i</math>, <math>j</math>, and <math>k</math> to be a set with the following three edges: {(i,j), (j,k), (i,k)}.  

We can define a triangle among the triple of vertices <math>i</math>, <math>j</math>, and <math>k</math> to be a set with the following three edges: {(i,j), (j,k), (i,k)}.  

我们可以通过'''<font color="#FF8000">边</font>'''集<math>((i,j),(j,k),(i,k))</math>，将由'''<font color="#FF8000">顶点</font>'''<math>i</math>,<math>j</math>和<math>k</math>组成的三元组定义为一个三角形。

我们可以通过边集<math>((i,j),(j,k),(i,k))</math>，将由顶点<math>i</math>,<math>j</math>和<math>k</math>组成的三元组定义为一个三角形。

We can also define the number of triangles that vertex <math>i</math> is involved in as <math>\delta (i)</math> and, as each triangle is counted three times, we can express the number of triangles in G as <math>\delta (G) = \frac{1}{3} \sum_{i\in V} \ \delta (i)</math>.  

We can also define the number of triangles that vertex <math>i</math> is involved in as <math>\delta (i)</math> and, as each triangle is counted three times, we can express the number of triangles in G as <math>\delta (G) = \frac{1}{3} \sum_{i\in V} \ \delta (i)</math>.  

We can also define the number of triangles that vertex <math>i</math> is involved in as <math>\delta (i)</math> and, as each triangle is counted three times, we can express the number of triangles in G as <math>\delta (G) = \frac{1}{3} \sum_{i\in V} \ \delta (i)</math>.  

We can also define the number of triangles that vertex <math>i</math> is involved in as <math>\delta (i)</math> and, as each triangle is counted three times, we can express the number of triangles in G as <math>\delta (G) = \frac{1}{3} \sum_{i\in V} \ \delta (i)</math>.  

我们也可以将'''<font color="#FF8000">顶点</font>'''<math>i</math>所涉及的三角形的数量定义为<math>\delta(i)</math>，并且由于每个三角形都被计数了三次，'''<font color="#FF8000">图</font>'''<math>G</math>中三角形的个数为<math>\delta (G) = \frac{1}{3} \sum_{i\in V} \ \delta (i)</math>。

我们也可以将顶点<math>i</math>所涉及的三角形的数量定义为<math>\delta(i)</math>，并且由于每个三角形都被计数了三次，我们可以将图<math>G</math>中三角形的个数表达为<math>\delta (G) = \frac{1}{3} \sum_{i\in V} \ \delta (i)</math>。

Assuming that triadic closure holds, only two strong edges are required for a triple to form. Thus, the number of theoretical triples that should be present under the triadic closure hypothesis for a vertex <math>i</math> is <math>\tau (i) = \binom{d_i}{2}</math>, assuming <math>d_i \ge 2</math>. We can express <math>\tau (G) = \frac{1}{3} \sum_{i\in V} \ \tau (i)</math>.

Assuming that triadic closure holds, only two strong edges are required for a triple to form. Thus, the number of theoretical triples that should be present under the triadic closure hypothesis for a vertex <math>i</math> is <math>\tau (i) = \binom{d_i}{2}</math>, assuming <math>d_i \ge 2</math>. We can express <math>\tau (G) = \frac{1}{3} \sum_{i\in V} \ \tau (i)</math>.

Assuming that triadic closure holds, only two strong edges are required for a triple to form. Thus, the number of theoretical triples that should be present under the triadic closure hypothesis for a vertex <math>i</math> is <math>\tau (i) = \binom{d_i}{2}</math>, assuming <math>d_i \ge 2</math>. We can express <math>\tau (G) = \frac{1}{3} \sum_{i\in V} \ \tau (i)</math>.

Assuming that triadic closure holds, only two strong edges are required for a triple to form. Thus, the number of theoretical triples that should be present under the triadic closure hypothesis for a vertex <math>i</math> is <math>\tau (i) = \binom{d_i}{2}</math>, assuming <math>d_i \ge 2</math>. We can express <math>\tau (G) = \frac{1}{3} \sum_{i\in V} \ \tau (i)</math>.

假设'''<font color="#FF8000">三元闭包</font>'''性质成立，则一个三元组仅需要两条'''<font color="#FF8000">强联系</font>'''便可形成三角形。 因此，在'''<font color="#FF8000">三元闭包</font>'''性质成立的前提下，理论上'''<font color="#FF8000">顶点</font>'''<math>i</math>所涉及的三角形的数量为<math>\tau(i) = \binom{d_i}{2}</math>， 假设<math>d_i \ge 2</math>。 我们可以表示<math>\tau(G) = \frac{1}{3} \sum_{i\in V} \ \tau(i)</math>。

假设三元闭包性质成立，则一个三元组仅需要两条强联系便可形成三角形。 因此，在三元闭包性质成立的前提下，理论上顶点<math>i</math>所涉及的三角形的数量为<math>\tau(i) = \binom{d_i}{2}</math>，假设<math>d_i \ge 2</math>。我们可以表示<math>\tau(G) = \frac{1}{3} \sum_{i\in V} \ \tau(i)</math>。

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.

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.

现在，对于具有<math>d_i \ge 2</math>的'''<font color="#FF8000">顶点</font>'''<math>i</math>，'''<font color="#FF8000">顶点</font>'''<math>i</math>的'''<font color="#FF8000">聚集系数</font>'''<math>c(i)</math> 是其拥有的三角形的占比，即<math>\frac{\delta(i)}{\tau(i)}</math>。 因此，'''<font color="#FF8000">图</font>'''<math>G</math>的'''<font color="#FF8000">聚集系数</font>'''<math>C(G)</math>由<math> C(G)=\frac {1}{N_2} \sum_{i \in V,d_i \ge 2}c(i)</math>给出，其中<math>N_2</math>是'''<font color="#FF8000">度</font>'''至少为2的'''<font color="#FF8000">顶点</font>'''数量。

现在，对于具有<math>d_i \ge 2</math>的顶点，顶点<math>i</math>的聚集系数是其拥有的三角形的占比，即<math>\frac{\delta(i)}{\tau(i)}</math>。 因此，图<math>G</math>的聚集系数<math>C(G)</math>由<math> C(G)=\frac {1}{N_2} \sum_{i \in V,d_i \ge 2}c(i)</math>给出，其中<math>N_2</math>是度至少为2的顶点数量。

==Transitivity==

==Transitivity==