Fig. 1
From: Revealing and exploiting hierarchical material structure through complex atomic networks
A network with three communities of five nodes each. Let the white, grey and black communities be C 1, C 2, C 3. Then A ss , the number of internal edges, is {8, 9, 9}. The sum of degrees of each community, A s is {18, 21, 21}, and the total number of edges is 30, giving a final value for Q of 0.532. An alternative partition, indicated by the dotted lines, has A ss = {18, 9} and A s = {39, 21}, giving Q = 0.355. As expected, the less intuitive partitioning gives a lower Q value
