itransitivity {inetwork} | R Documentation |
The clustering coefficient of each vertex of an undirected and unweighted network is calculated given the network's adjacency matrix
itransitivity(A)
A |
a symmetric adjacency matrix with elements zeros or ones representing an undirected and unweighted network |
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.
c |
an array holding the clustering coefficients of the vertices |
Ck |
the averaged c's for the vertices having the same degree k |
For large networks consisting of 700 vertices, the calculation can take ten minutes. The computation time/resource scales as O(n^3).
Sun-Chong Wang