Cycle-tree guided attack of random K-core: Spin glass model and efficient message-passing algorithm

TL;DR

This paper introduces a novel cycle-tree guided attack algorithm for efficiently identifying minimal vertex sets that collapse the K-core of a graph, using spin-glass models and message-passing techniques.

Contribution

It presents a new cycle-tree based message-passing algorithm for the K-core attack problem, connecting spin-glass theory with network robustness analysis.

Findings

CTGA outperforms existing methods in efficiency and accuracy

Algorithm verified on random graph ensembles

Transforms dynamic processes into static structural patterns

Abstract

The K-core of a graph is the maximal subgraph within which each vertex is connected to at least K other vertices. It is a fundamental network concept for understanding threshold cascading processes with a discontinuous percolation transition. A minimum attack set contains the smallest number of vertices whose removal induces complete collapse of the K-core. Here we tackle this prototypical optimal initial-condition problem from the spin-glass perspective of cycle-tree maximum packing and propose a cycle-tree guided attack (CTGA) message-passing algorithm. The good performance and time efficiency of CTGA are verified on the regular random and Erd\"os-R\'enyi random graph ensembles. Our central idea of transforming a long-range correlated dynamical process to static structural patterns may also be instructive to other hard optimization and control problems.