Document Type

Article

Publication Date

8-6-2013

Journal or Book Title

Journal of Statistical Mechanics: Theory and Experiment

First Page

P08001

DOI

10.1088/1742-5468/2013/08/P08001

Abstract

We study a simple model of dynamic networks, characterized by a set preferred degree, κ. Each node with degree k attempts to maintain its κ and will add (cut) a link with probability w(k;κ) (1 − w(k;κ)). As a starting point, we consider a homogeneous population, where each node has the same κ, and examine several forms of w(k;κ), inspired by Fermi–Dirac functions. Using Monte Carlo simulations, we find the degree distribution in the steady state. In contrast to the well known Erdős–Rényi network, our degree distribution is not a Poisson distribution; yet its behavior can be understood by an approximate theory. Next, we introduce a second preferred degree network and couple it to the first by establishing a controllable fraction of inter-group links. For this model, we find both understandable and puzzling features. Generalizing the prediction for the homogeneous population, we are able to explain the total degree distributions well, but not the intra- or inter-group degree distributions. When monitoring the total number of inter-group links, X, we find very surprising behavior. X explores almost the full range between its maximum and minimum allowed values, resulting in a flat steady-state distribution, reminiscent of a simple random walk confined between two walls. Both simulation results and analytic approaches will be discussed.

Comments

This is an author's manuscript of an article from Journal of Statistical Mechanics: Theory and Experiment (2013): P08001, doi:10.1088/1742-5468/2013/08/P08001.

Copyright Owner

IOP Publishing Ltd. and SISSA Medialab srl

Language

en

File Format

application/pdf

Included in

Physics Commons

Share

COinS