Infinite Ergodic Walks in Finite Connected Undirected Graphs

Date
2021
Journal Title
Journal ISSN
Volume Title
Publisher
MDPI
Abstract

The micro-canonical, canonical, and grand canonical ensembles of walks defined in finite connected undirected graphs are considered in the thermodynamic limit of infinite walk length. As infinitely long paths are extremely sensitive to structural irregularities and defects, their properties are used to describe the degree of structural imbalance, anisotropy, and navigability in finite graphs. For the first time, we introduce entropic force and pressure describing the effect of graph defects on mobility patterns associated with the very long walks in finite graphs; navigation in graphs and navigability to the nodes by the different types of ergodic walks; as well as node’s fugacity in the course of prospective network expansion or shrinking.

Description
This paper is an extended version of our paper published in The 1st Online Conference on Nonlinear Dynamics and Complexity, Central Time Zone, USA, 23–25 November 2020.
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords
Statistical Ensembles of Walks, Entropic Force and Pressure, Graph's Navigation, Graph Node's Navigability, Graph Node's Fugacity
Citation
Volchenkov D. Infinite Ergodic Walks in Finite Connected Undirected Graphs. Entropy. 2021; 23(2):205. https://doi.org/10.3390/e23020205
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