Eur. Phys. J. B 63, 273-278 (2008)
https://doi.org/10.1140/epjb/e2008-00236-4

Heterogeneous network with distance dependent connectivity

¹ Department of Mathematics, Physics and Informatics, Mlynská dolina, 842 48 Bratislava, Slovak Republic
² Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland

Corresponding authors: ^a matus.medo@unifr.ch - ^b jano.smrek@gmail.com

Received: 31 January 2008
Revised: 7 May 2008
Published online: 20 June 2008

Abstract

We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the basic model is sharply peaked around its mean value. Since the model was originally developed to mimic the social network of acquaintances, to broaden the degree distribution we propose its generalization. We show that when heterogeneity is introduced to the model, it is possible to obtain fat tails of the degree distribution. Meanwhile, the small-world phenomenon present in the basic model is not affected. To support our claims, both analytical and numerical results are obtained.