B = modmat(G) find modularity matrix of the undirected graph. Each
element in the matrix is defined as:
k_i * k_j
b_ij = A_ij - -----------
2 * m
k_i, k_j: vertices degree of i and j
A_ij: adjacency, 1 if node i and node j are conected, 0 otherwise
m: the total number of edges
B = modmat(G, ng) incremental modularity matrix of subgroup of nodes ng
Example
G = set(G, 'directed', 0); % convert to undirected graph
G = simple(G); % convert to simple graph
q = modmat(G)
Example
% binary spectral partitioning
mod = modmat(G);
[v, e] = eig(mod);
d = []; for k = 1:size(G,1), d(k) = e(k,k); end % take diagonal
[maxeig, maxeigidx] = max(d);
s = sign(v(:,maxeigidx)); % partitioning vector into two groups
q = modularity(G, s); % calculate modularity matrix
G = set(G, 'nodecolor', s); % change node color according to grouping
plot(G)
See Also
SPECBIPART, MODULARITY, SIMPLE.