Eur. Phys. J. B 59, 133-139 (2007)
https://doi.org/10.1140/epjb/e2007-00270-8

Phase transitions in social networks

Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland

Corresponding author: ^a fronczak@if.pw.edu.pl

Received: 10 May 2007
Revised: 28 August 2007
Published online: 5 October 2007

Abstract

We study a model of network with clustering and desired node degree. The original purpose of the model was to describe optimal structures of scientific collaboration in the European Union. The model belongs to the family of exponential random graphs. We show by numerical simulations and analytical considerations how a very simple Hamiltonian can lead to surprisingly complicated and eventful phase diagram.