Evolving network – simulation study

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 informati...

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Bibliographic Details
Published in:The European physical journal. B, Condensed matter physics Condensed matter physics, 2005-01, Vol.48 (4), p.547-555
Main Author: Makowiec, D
Format: Article
Language:English
Subjects:
Algorithms
Apexes
Evolution
Graph theory
Tangling
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Summary: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.
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2006-00008-2