Eur. Phys. J. B (2014) 87: 161
https://doi.org/10.1140/epjb/e2014-40800-7

Regular Article

The gateway coefficient: a novel metric for identifying critical connections in modular networks

Department of Applied Mathematics, Western University, London, N6A 5B7, Canada

^a e-mail: eruizvar@uwo.ca

Received: 30 August 2013
Received in final form: 13 May 2014
Published online: 23 July 2014

Abstract

The modular structure of a complex network is an important and well-studied topological property. Within this modular framework, particular nodes which play key roles have been previously identified based on the node’s degree, and on the node’s participation coefficient, a measure of the diversity of a node’s intermodular connections. In this contribution, we develop a generalization of the participation coefficient, called the gateway coefficient, which measures not only the diversity of the intermodular connections, but also how critical these connections are to intermodular connectivity; in brief, nodes which form rare or unique “gateways” between sparsely connected modules rank highly in this measure. We illustrate the use of the gateway coefficient with simulated networks with defined modular structure, as well as networks obtained from air transportation data and functional neuroimaging.