TY - JOUR

T1 - Mean-field analysis of directed modular networks

AU - Moriya, Satoshi

AU - Yamamoto, Hideaki

AU - Akima, Hisanao

AU - Hirano-Iwata, Ayumi

AU - Kubota, Shigeru

AU - Sato, Shigeo

N1 - Funding Information:
This study was supported by the Cooperative Research Project Program of the Research Institute of Electrical Communication, Tohoku University; the Program on Open Innovation Platform with Enterprises, Research Institute and Academia (OPERA) from Japan Science and Technology Agency (JST); and JSPS KAKENHI (Grant Nos. 17K18864, 18J12197, and 18H03325).

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

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U2 - 10.1063/1.5044689

DO - 10.1063/1.5044689

M3 - Article

C2 - 30709116

AN - SCOPUS:85060910964

VL - 29

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 1

M1 - 013142

ER -