Optimal Disruption of Complex Networks

TL;DR

This paper introduces a physics-inspired method to efficiently identify minimal sets of arcs to disrupt in complex networks, effectively breaking feedback cycles and fragmenting strongly connected components.

Contribution

It maps the network disruption problem to the minimal feedback arc set problem and applies spin glass theory for a novel, effective solution approach.

Findings

Outperforms local heuristics and simulated annealing in network disruption tasks.

Works effectively on both random and real-world networks.

Provides a scalable method for controlling complex systems.

Abstract

The collection of all the strongly connected components in a directed graph, among each cluster of which any node has a path to another node, is a typical example of the intertwining structure and dynamics in complex networks, as its relative size indicates network cohesion and it also composes of all the feedback cycles in the network. Here we consider finding an optimal strategy with minimal effort in removal arcs (for example, deactivation of directed interactions) to fragment all the strongly connected components into tree structure with no effect from feedback mechanism. We map the optimal network disruption problem to the minimal feedback arc set problem, a non-deterministically polynomial hard combinatorial optimization problem in graph theory. We solve the problem with statistical physical methods from spin glass theory, resulting in a simple numerical method to extract sub-optimal disruption arc sets with significantly better results than a local heuristic method and a simulated annealing method both in random and real networks. Our results has various implications in controlling and manipulation of real interacted systems.