Deterministic walks in random networks: an application to thesaurus graphs
O. Kinouchi, A. S. Martinez, G. F. Lima, G. M. Lourenco, S. Risau-Gusman
Abstract
In a landscape composed of N randomly distributed sites in Euclidean space, a walker (``tourist'') goes to the nearest one that has not been visited in the last τsteps. This procedure leads to trajectories composed of a transient part and a final cyclic attractor of period p. The tourist walk presents universal aspects with respect to τand can be done in a wide range of networks that can be viewed as ordinal neighborhood graphs. As an example, we show that graphs defined by thesaurus dictionaries share some of the statistical properties of low dimensional (d=2) Euclidean graphs and are easily distinguished from random graphs. This approach furnishes complementary information to the usual clustering coefficient and mean minimum separation length.
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