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arXiv · 1610.04549

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

H. L. Casa Grande·M. Cotacallapa·M. O. Hase
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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.

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BibTeXRIS

H. L. Casa Grande, M. Cotacallapa, M. O. Hase. 2016-10-14. Random walk in degree space and the time-dependent Watts-Strogatz model. https://doi.org/10.1103/physreve.95.012321

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