Volume 108, Number 4, November 2014
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||20 November 2014|
Characterizing the efficiency and catalytic effects of modular structures in information propagation
1 School of Mathematical Sciences, Peking University - 100871, Beijing, China
2 Key Laboratory of Mathematics, Informatics and Behavioral Semantics of Ministry of Education, Beihang University - 100191, Beijing, China
3 School of Mathematics and Systems Science, Beihang University - 100191, Beijing, China
Received: 24 June 2014
Accepted: 31 October 2014
Information propagation plays an important role in the dynamic processes on complex networks. Here we consider the information propagation process under the scale of pre-divided modular structures. In this scale, the efficiency of the module can be characterized by the global mean module first-passage time (GMMFPT), and we derive the analytical expression of GMMFPT by the help of singular value decomposition and the generating function methods. A numerical simulation is performed to testify the validity of GMMFPT in characterizing the modular efficiency in information propagation. Under the modular scale, a novel phenomenon associated with GMMFPT, the so-called catalytic effects, is present with the increase of mixing parts. The catalytic effect reveals the vital function of the mixing parts of modules in information propagation and also indicates the critical point where an invisible abrupt transition of the network structures occurs, which provides a potential guideline for the pursuit of the optimal efficiency.
PACS: 89.75.-k – Complex systems / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.70.Ln – Nonequilibrium and irreversible thermodynamics
© EPLA, 2014
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