Finding community structure in spatially constrained complex networks

Abstract

One feature discovered in the study of complex networks is community structure, in which vertices are gathered into several groups where more edges exist within groups than between groups. Many approaches have been developed for identifying communities; these approaches essentially segment networks based on topological structure or the attribute similarity of vertices, while few approaches consider the spatial character of the networks. Many complex networks are spatially constrained such that the vertices and edges are embedded in space. In geographical space, nearer objects are more related than distant objects. Thus, the relations among vertices are defined not only by the links connecting them but also by the distance between them. In this article, we propose a geo-distance-based method of detecting communities in spatially constrained networks to identify communities that are both highly topologically connected and spatially clustered. The algorithm is based on the fast modularity maximisation (CNM) algorithm. First, we modify the modularity to geo-modularity Q^geo by introducing an edge weight that is the inverse of the geographic distance to the power of n. Then, we propose the concept of a spatial clustering coefficient as a measure of clustering of the network to determine the power value n of the distance. The algorithm is tested with China air transport network and BrightKite social network data-sets. The segmentation of the China air transport network is similar to the seven economic regions of China. The segmentation of the BrightKite social network shows the regionality of social groups and identifies the dynamic social groups that reflect users’ location changes. The algorithm is useful in exploring the interaction and clustering properties of geographical phenomena and providing timely location-based services for a group of people.

Keywords:

• complex network
• spatial constraint
• community
• modularity

Acknowledgements

The authors thank the anonymous reviewers whose remarks greatly improved the presentation of this work. This research was supported by the National Natural Science Foundation of China [Grants 41171296 and 41371380].