Mean-field analysis of directed modular networks

Satoshi Moriya, Hideaki Yamamoto, Hisanao Akima, Ayumi Hirano-Iwata, Shigeru Kubota, Shigeo Sato

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We considered a modular network with a binomial degree distribution and related the analytical relationships of the network properties (modularity, average clustering coefficient, and small-worldness) with structural parameters that define the network, i.e., number of nodes, number of modules, average node degree, and ratio of intra-modular to total connections. Even though modular networks are universally found in real-world systems and are consequently of broad interest in complex network science, the relationship between network properties and structural parameters has not yet been formulated. Here, we show that a series of equations for predicting the network properties can be related using a mean-field connectivity matrix that is defined on the basis of the structural parameters in the network generation algorithm. The theoretical results are then compared with values calculated numerically using the original connectivity matrix and are found to agree well, except when the connections between modules are sparse. Representation of the structure of the network using simple parameters is expected to be conducive for elucidating the structure-dynamics relationship.

Original languageEnglish
Article number013142
JournalChaos
Volume29
Issue number1
DOIs
Publication statusPublished - 2019 Jan 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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