Functional units in complex networks: beyond cohesive modules

A large amount of networks are found to divide naturally into modules or communities within which the network connections are tight but between which they are sparser. However, it is still not clear that whether sparse modules in which the nodes are sparsely connected internally and densely connected with other sparse or cohesive modules possibly exist and have functional meaning in complex networks. In this study, we first test BinTree Seeking method that detects both cohesive and sparse modules in a network on 4 networks with known modular structure. And then, we further study modular structure of 23 complex networks of different types and scales, and promising results indeed reveal that the sparse modules composed by the cohesively isolated nodes widely co-exist with the cohesive modules. Furthermore, the two types of modules are found often spatially closely related with each other. Compared with the cohesive modules, sizes of sparse ones are generally smaller.