Figure 5. Effect of varying the temporal divergence on the distance from the ground truth for benchmark evolving network described in Fig. 4.

The average loss in modularity (over all snapshots) due to the estrangement constraint decreases as the constraint is relaxed. Estrangement, on the other hand, increases as the constraint is relaxed. The distance of the obtained temporal partition (labeled on the right y axis) from the benchmark ground truth as quantified by VI is lowest around δ = 0.05. The range of this distance varies roughly between 2.5 and 3.1 (labeled on the right y axis) as δ is varied, which is significant since VI is a logarithmic measure (see Methods). Thus, by varying the constraint on estrangement we get a different set of temporal communities which could all be meaningful. The average loss in modularity relative to the average gain in estrangement indicates the range of values of δ which might yield meaningful temporal communities.