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The clustering coefficient is a measure of an "all-my-friends-know-each-other" property. This is sometimes described as the friends of my friends are my friends. More precisely, the clustering coefficient of a node is the ratio of existing links connecting a node's neighbors to each other to the maximum possible number of such links. The clustering coefficient for the entire network is the average of the clustering coefficients of all the nodes. A high clustering coefficient for a network is another indication of a [[Small-world experiment|small world]].
The clustering coefficient is a measure of an "all-my-friends-know-each-other" property. This is sometimes described as the friends of my friends are my friends. More precisely, the clustering coefficient of a node is the ratio of existing links connecting a node's neighbors to each other to the maximum possible number of such links. The clustering coefficient for the entire network is the average of the clustering coefficients of all the nodes. A high clustering coefficient for a network is another indication of a [[Small-world experiment|small world]].
聚集系数是表示“我所有的朋友都互相认识”这样一种性质的指标。有时候也被表述为“我朋友的朋友也是我的朋友”。更准确地说，节点的聚类系数是该节点的相邻节点之间的现有连接数与其最大可能连接数之比。整个网络的聚集系数是所有节点的聚集系数的平均值。网络的高聚集系数是[[小世界实验|小世界]]的另一个标志。
:<math>{\binom {k}{2}} = {{k(k-1)}\over 2}\,.</math>
:<math>{\binom {k}{2}} = {{k(k-1)}\over 2}\,.</math>
第 <math>i</math> 个节点的聚集系数为
:<math>C_i = {2e_i\over k_i{(k_i - 1)}}\,,</math>
:<math>C_i = {2e_i\over k_i{(k_i - 1)}}\,,</math>
其中 <math>k_i</math> 是节点 <math>i</math> 的相邻节点数， <math>e_i</math> 是这些相邻节点数之间的连接数。相邻接点见最大可能的连接数为
其中 <math>k_i</math> 是第 <math>i</math> 个节点的相邻节点数， <math>e_i</math> 是这些相邻节点数之间的连接数。相邻节点之间的最大可能连接数为
:<math>{\binom {k}{2}} = {{k(k-1)}\over 2}\,.</math>
:<math>{\binom {k}{2}} = {{k(k-1)}\over 2}\,.</math>
From a probabalistic standpoint, the expected local clustering coefficient is the likelihood of a link existing between two arbitrary neighbors of the same node.
From a probabalistic standpoint, the expected local clustering coefficient is the likelihood of a link existing between two arbitrary neighbors of the same node.
从概率的角度来看，期望的局部聚集系数是同一节点的任意两个相邻节点之间存在连接的可能性。
=== 连通性 ===
=== 连通性 ===