Mean-field analysis of directed modular networks

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

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号013142
ジャーナルChaos
29
1
DOI
出版ステータスPublished - 2019 1 1

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 物理学および天文学(全般)
  • 応用数学

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