Using NonBacktracking Expansion to Analyze k-core Pruning Process

TL;DR

This paper introduces the NonBacktracking Expansion Branch method as a simple, intuitive approach to analyze the k-core pruning process on graphs, including correlated networks, overcoming the complexity of traditional methods.

Contribution

The paper presents a novel analytical method for k-core pruning analysis that is simpler and extendable to correlated networks, unlike previous complex approaches.

Findings

Provides a simple, intuitive solution to k-core pruning analysis.

Extends the analysis to correlated networks.

Offers an alternative to traditional generating functions and degree distribution methods.

Abstract

We induce the NonBacktracking Expansion Branch method to analyze the k-core pruning process on the monopartite graph G which does not contain any self-loop or multi-edge. Different from the traditional approaches like the generating functions or the degree distribution evolution equations which are mathematically difficult to solve, this method provides a simple and intuitive solution of the k-core pruning process. Besides, this method can be naturally extended to study the k-core pruning process on correlated networks, which is among the few attempts to analytically solve the problem.