Figure 1

Examples of disjoint modules and overlapping modules. The network (a) has two disjoint modules detected by disconnecting two interconnecting edges ⟨L, N〉 and ⟨K, M〉. The intra-connection rates of these modules are both 0.89. Each module includes not only core nodes (black color) but also peripheral nodes (white color). The network (b) has two overlapping modules {A, B, ⋯, L, M, N, O, P} and {I, J, K, L, M, ⋯, W, X}. The intra-connection rates of these modules are both 0.87, whereas those of two disjoint sub-graphs by disconnecting ⟨ L, P⟩, ⟨L, N⟩, ⟨K, M⟩ and ⟨J, M⟩ are 0.81. The intra-connection rate represents the proportion of the number of connections among the nodes in a module to the number of all connections starting from the nodes.