Figure 4. Estrangement confined modularity maximization allows detection of temporal communities in the benchmark network presented in Fig. 3.

The markovian evolution parameters (described in text) for this network are set to p = 0.6 and q = p p_c/(1 – p_c) = 0.4, which preserve the edge density (p_c = 0.4) within a dense group (unless it ceases to exist). The density of connections in the random network background is p_r = 0.05. The ability to detect the temporal communities diminishes as the constraint on estrangement is relaxed (δ → 1) with the poorest results obtained for independent modularity maximization (δ = 1).