Random walk in degree space and the time-dependent Watts-Strogatz model

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 Erdös-Rényi 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.

References in corpus (3)

• The structure and dynamics of multilayer networks
• Critical phenomena in complex networks
• The entropy of randomized network ensembles