But overlapping communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community(ies), and less likely to be connected if they do not share communities.
However, overlapping communities are still accepted. The expanded definition hinges on the notion that node pairs are more likely to be connected when they both reside in the same community(ies), and less likely to connect if they do not belong to any shared communities.