Ranking nodes according to their path-complexity

TL;DR

This paper introduces a new entropy-based centrality measure for nodes in Markov chains by analyzing path complexity and fixed point entropy, providing a novel way to rank nodes based on their path properties.

Contribution

It proposes a macroscopic entropy on path states and develops a fixed point entropy approach, offering a new centrality measure for Markov chain analysis.

Findings

Introduces a path-based entropy measure for Markov chains

Derives a fixed point entropy for node ranking

Provides a new centrality approach based on path complexity

Abstract

Thermalization is one of the most important phenomena in statistical physics. Often, the transition probabilities between different states in the phase space is or can be approximated by constants. In this case, the system can be described by Markovian transition kernels, and when the phase space is discrete, by Markov chains. In this paper, we introduce a macroscopic entropy on the states of paths of length $k$ and, studying the recursion relation, obtain a fixed point entropy. This analysis leads to a centrality approach to Markov chains entropy.