itransitivity {inetwork}R Documentation

Clustering Coefficient

Description

The clustering coefficient of each vertex of an undirected and unweighted network is calculated given the network's adjacency matrix

Usage

itransitivity(A)

Arguments

A a symmetric adjacency matrix with elements zeros or ones representing an undirected and unweighted network

Details

The clustering coefficient or transitivity c_i of vertex i is defined as

c_i = (1/(k_i(k_i-1))) sum_jh (A_ij*A_ih*A_jh)

where k_i is the degree of vertex i and A_ij the adjacency matrix of the network. The clustering coefficient measures the connectivity of the neighboring vertices of a vertex. A decreasing c with k indicates that the network is hierarchical as observed in many nonrandom networks.

Value

c an array holding the clustering coefficients of the vertices
Ck the averaged c's for the vertices having the same degree k

Note

For large networks consisting of 700 vertices, the calculation can take ten minutes. The computation time/resource scales as O(n^3).

Author(s)

Sun-Chong Wang

See Also

iassortativity


[Package inetwork version 1.2 Index]