An energy-based model for spatial social networks

Abstract

In the past decade, thanks to abundant data and adequate software tools, complex networks have been thoroughly investigated in many disciplines. Most of this work has dealt with networks in which distances do not have physical meaning and are just dimensionless quantities measured in terms of edge hops. However, in many cases the physical space in which networks are embedded and the actual distances between nodes are important, such as in geographical and transportation networks. The Random Geometric Graph (RGG) is a standard spatial network model that plays a role for spatial networks similar to the one played by the Erdös Ŕenyi random graph for relational ones. In this work we present an extension of the RGG construction to define a new model to build bi-dimensional spatial networks based on energy as realistic constraint to create the links. The constructed networks have several properties in common with those of actual social networks.