Characterizing the efficiency and catalytic effects of modular structures in information propagation

摘要: Information propagation plays an important role in the dynamic processes on complex networks. Here we consider information process under scale of pre-divided modular structures. In this scale, efficiency module can be characterized by global mean first-passage time (GMMFPT), and derive analytical expression GMMFPT help singular value decomposition generating function methods. A numerical simulation is performed to testify validity characterizing propagation. Under a novel phenomenon associated with GMMFPT, so-called catalytic effects, present increase mixing parts. The effect reveals vital parts modules also indicates critical point where invisible abrupt transition network structures occurs, which provides potential guideline for pursuit optimal efficiency.