Modularity Q, originally defined for unweighted graphs [38], measures the difference between the fraction of arcs connecting nodes belonging to the same community in the actual graph and its expected value in a random graph. Modularity Q in the case of directed weighted graphs reads [39]: (4)where the function yields 1 if vertices i and j are in the same community C (here in the same brain, B1 or B2), and 0 otherwise, as in the case of divisibility D. As a result, in the expression of Q, the only contributions come from couples of nodes belonging to the same brain. Hence, the higher is the value of modularity, the better is the partition of the networks into the two communities B1 and B2.
