Finding multiple core-periphery pairs in networks.

Sadamori Kojaku,Naoki Masuda

doi:10.1103/physreve.96.052313

Abstract

With a core-periphery structure of networks, core nodes are densely interconnected, peripheral nodes are connected to core nodes to different extents, and peripheral nodes are sparsely interconnected. Core-periphery structure composed of a single core and periphery has been identified for various networks. However, analogous to the observation that many empirical networks are composed of densely interconnected groups of nodes, i.e., communities, a network may be better regarded as a collection of multiple cores and peripheries. We propose a scalable algorithm to detect multiple nonoverlapping groups of core-periphery structure in a network. We illustrate our algorithm using synthesized and empirical networks. For example, we find distinct core-periphery pairs with different political leanings in a network of political blogs and separation between international and domestic subnetworks of airports in some single countries in a worldwide airport network.

Highlights

Many complex systems can be expressed as networks in which a node represents an object and an edge represents the relationship between two objects
Core-periphery structure is another mesoscale structure of networks, with which we view a network as being composed of two groups of nodes called the core and periphery
We report the results obtained from the two-step algorithm and those obtained from the divisive algorithm in Appendix B

Summary

Introduction

Many complex systems can be expressed as networks in which a node represents an object (e.g., person, web page, protein) and an edge represents the relationship between two objects (e.g., friendship, hyperlink, physical interaction). A network can be characterized by microscale, mesoscale, and macroscale structural patterns such as the degree (i.e., the number of edges that a node has), clustering coefficient, and diameter [1,2]. Among various structural properties of networks, community structure is a representative mesoscale structure of networks [3]. A community is a group of nodes that are densely interconnected and sparsely connected to nodes in different communities. Core-periphery structure is another mesoscale structure of networks, with which we view a network as being composed of two groups of nodes called the core and periphery. A core and community are both groups of densely interconnected nodes but have a difference; a core connects densely to its periphery, whereas a community is not densely connected to other nodes outside it.

Methods

Results

Conclusion