Eur. Phys. J. B 48, 547-555 (2005)
https://doi.org/10.1140/epjb/e2006-00008-2

Evolving network – simulation study

From regular lattice to scale free network

Institute of Theoretical Physics and Astrophysics, Gdańsk University, ul. Wita Stwosza 57, 80-952 Gdansk, Poland

Corresponding author: ^a fizdm@univ.gda.pl

Received: 25 May 2005
Revised: 10 October 2005
Published online: 19 January 2006

Abstract

The Watts-Strogatz algorithm of transferring the square lattice to a small world network is modified by introducing preferential rewiring constrained by connectivity demand. The evolution of the network is two-step: sequential preferential rewiring of edges controlled by p and updating the information about changes done. The evolving system self-organizes into stationary states. The topological transition in the graph structure is noticed with respect to p. Leafy phase – a graph formed by multiple connected vertices (graph skeleton) with plenty of leaves attached to each skeleton vertex emerges when p is small enough to pretend asynchronous evolution. Tangling phase where edges of a graph circulate frequently among low degree vertices occurs when p is large. There exist conditions at which the resulting stationary network ensemble provides networks which degree distribution exhibit power-law decay in large interval of degrees.