Random walk in degree space and the time-dependent Watts-Strogatz model
Physics and Society
2017-01-25 v2 Statistical Mechanics
Social and Information Networks
Abstract
In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erd\"os-R\'enyi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.
Cite
@article{arxiv.1610.04549,
title = {Random walk in degree space and the time-dependent Watts-Strogatz model},
author = {H. L. Casa Grande and M. Cotacallapa and M. O. Hase},
journal= {arXiv preprint arXiv:1610.04549},
year = {2017}
}