Eur. Phys. J. B 38, 305-309 (2004)
https://doi.org/10.1140/epjb/e2004-00018-0

Multi-component static model for social networks

School of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea

Corresponding author: ^a kahng@phya.snu.ac.kr

Received: 27 October 2003
Published online: 17 February 2004

Abstract

The static model was introduced to generate a scale-free network. In the model, N number of vertices are present from the beginning. Each vertex has its own weight, representing how much the vertex is influential in a system. The static model, however, is not relevant, when a complex network is composed of many modules such as communities in social networks. An individual may belong to more than one community and has distinct weights for each community. Thus, we generalize the static model by assigning a q-component weight on each vertex. We first choose a component among the q components at random and a pair of vertices is linked with a color μ according to their weights of the component as in the static model. A fraction of the entire edges is connected following this way. The remaining fraction f is added with (q+1)-th color as in the static model but using the maximum weights among the q components each individual has. The social activity with such maximum weights is an essential ingredient to enhance the assortativity coefficient as large as the ones of real social networks.