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Random walk in degree space and the time-dependent Watts-Strogatz model
H L Casa Grande1, M Cotacallapa1,2, M O Hase1
1Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Béttio 1000, 03828-000 São Paulo, Brazil.
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 Erdős-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.
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