Symbolic walk in regular networks

Abstract

We find that a symbolic walk (SW) - performed by a walker with memory given by a Bernoulli shift - is able to distinguish between the random or chaotic topology of a given network. We show this result by means of studying the undirected baker network, which is defined by following the Ulam approach for the baker transformation in order to introduce the effect of deterministic chaos into its structure. The chaotic topology is revealed through the central role played by the nodes associated with the positions corresponding to the shortest periodic orbits of the generating map. They are the overwhelmingly most visited nodes in the limit cycles at which the SW asymptotically arrives. Our findings contribute to linking deterministic chaotic dynamics with the properties of networks constructed using the Ulam approach.