title: 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 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.
authors.affiliation: Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Béttio 1000, 03828-000 São Paulo, Brazil.
authors.forename: H L
authors.initials: HL
authors.lastname: Casa Grande
authors.affiliation: Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Béttio 1000, 03828-000 São Paulo, Brazil.|Instituto Nacional de Pesquisas Espaciais, 12227-010, São José dos Campos, São Paulo, Brazil.
authors.forename: M
authors.initials: M
authors.lastname: Cotacallapa
authors.affiliation: Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Béttio 1000, 03828-000 São Paulo, Brazil.
authors.forename: M O
authors.initials: MO
authors.lastname: Hase