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→Clustering coefficient
=== Clustering coefficient ===
=== Clustering coefficient ===
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 of the <math>i</math>'th node is
:<math>C_i = {2e_i\over k_i{(k_i - 1)}}\,,</math>
where <math>k_i</math> is the number of neighbours of the <math>i</math>'th node, and <math>e_i</math> is the number of connections between these neighbours. The maximum possible number of connections between neighbors is, then,
:<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.
===聚集系数===
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]].