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Trajectory Data Analyses for Pedestrian Space-time Activity Study
Published on: February 25, 2013
First-passage process in degree space for the time-dependent Erdős-Rényi and Watts-Strogatz models
1Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Béttio 1000, 03828-000 São Paulo, Brazil.
Abstract:
In this work, we investigate the temporal evolution of the degree of a given vertex in a network by mapping the dynamics into a random walk problem in degree space. We analyze when the degree approximates a preestablished value through a parallel with the first-passage problem of random walks. The method is illustrated on the time-dependent versions of the Erdős-Rényi and Watts-Strogatz models, which were originally formulated as static networks. We have succeeded in obtaining an analytic form for the first and the second moments of the first-passage time and showing how they depend on the size of the network. The dominant contribution for large networks with N vertices indicates that these quantities scale on the ratio N/p, where p is the linking probability.
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