Newman-Girvan modularity Q (alias of Sgtmodq)

This module is an ALIAS. Modularity is implemented once, in Sgtmodq; this entry point delegates.

Usage

Modulq(G, communities)

Arguments

G

Symmetric adjacency or weight matrix.

communities

Integer community label per node.

Value

List with Q, estimate, n_communities, n.

Details

Q = (1 / 2m) sum_ij (A_ij - k_i k_j / 2m) delta(c_i, c_j) with 2m = sum_ij A_ij. The configuration-model null term is why a single all-node community scores exactly zero however dense the graph.

References

Newman and Girvan (2004), Physical Review E 69, 026113, doi:10.1103/PhysRevE.69.026113 .

Examples

A <- matrix(0, 6, 6); A[1:3, 1:3] <- 1; A[4:6, 4:6] <- 1; A[3, 4] <- A[4, 3] <- 1; diag(A) <- 0
Modulq(A, communities = c(1, 1, 1, 2, 2, 2))$Q
#> [1] 0.3571429