Symbolic walk in regular networks

TL;DR

This paper demonstrates that a symbolic walk with memory can distinguish between random and chaotic network topologies, revealing the influence of deterministic chaos on network structure through node visitation patterns.

Contribution

It introduces a method using symbolic walks to identify chaotic topology in networks, specifically analyzing the baker network via the Ulam approach.

Findings

Symbolic walk identifies chaotic topology through node visitation patterns.

Nodes associated with shortest periodic orbits are most visited.

Chaotic topology is linked to deterministic chaos in network structure.

Abstract

We find that a symbolic walk (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 symbolic walker asymptotically arrives. Our findings contribute to link deterministic chaotic dynamics with the properties of networks constructed using the Ulam approach.