Eur. Phys. J. B (2014) 87: 212
https://doi.org/10.1140/epjb/e2014-50242-x

Regular Article

Percolation in the classical blockmodel

Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland

^a e-mail: fronczak@if.pw.edu.pl

Received: 10 April 2014
Received in final form: 15 July 2014
Published online: 17 September 2014

Abstract

Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation transition in the classical blockmodel has not been examined so far, although the phenomenon has been studied in a variety of much more complicated models of interconnected and multiplex networks. In this paper we derive the self-consistent equation for the size the global percolation cluster in the classical blockmodel. We also find the condition for percolation threshold which characterizes the emergence of the giant component. We show that the discussed percolation phenomenon may cause unexpected problems in a simple optimization process of the multilevel network construction. Numerical simulations confirm the correctness of our theoretical derivations.