LEARNING TO BOOST RESILIENCE OF COMPLEX NET-WORKS VIA NEURAL EDGE REWIRING

Abstract

The resilience of complex networks, a critical structural characteristic in network science, measures the network's ability to withstand noise corruption and structural changes. Improving resilience typically resorts to minimal modifications of the network structure via degree-preserving edge rewiring-based methods. Despite their effectiveness, existing methods are learning-free, sharing the limitation of transduction: a learned edge rewiring strategy from one graph cannot be generalized to another. Such a limitation cannot be trivially addressed by existing graph neural networks (GNNs)-based approaches since there is no rich initial node features for GNNs to learn meaningful representations. However, neural edge rewiring relies on GNNs for obtaining meaningful representations from pure graph topologies to select edges. We found existing GNNs degenerate remarkably with only pure topologies on the resilience task, leading to the undesired infinite action backtracking. In this work, inspired by persistent homology, we specifically design a variant of GNN called FireGNN for learning inductive edge rewiring strategies. Based on meaningful representations from FireGNN, we develop the first end-toend inductive method, ResiNet, to discover resilient network topologies while balancing network utility. ResiNet reformulates network resilience optimization as a Markov decision process equipped with edge rewiring action space and learns to select correct edges successively. Extensive experiments demonstrate that ResiNet achieves a near-optimal resilience gain on various graphs while balancing the utility and outperforms existing approaches by a large margin.

1. INTRODUCTION

Network systems, such as infrastructure systems and supply chains, are vulnerable to malicious attacks. To provide reliable services when facing natural disasters or targeted attacks, networked systems should continue to function and maintain an acceptable level of utility when the network partially fails. Network resiliencefoot_0 , in the context of network science, is a measurement characterizing the ability of a network system to defend itself from such failures and attacks (Schneider et al., 2011) . Studying the resilience of complex networks has found wide applications in many fields, ranging from ecology (Sole & Montoya, 2001) , biology (Motter et al., 2008) , economics (Haldane & May, 2011) to engineering (Albert et al., 2004) . To improve network resilience, many learning-free optimization methods have been proposed, typically falling into the categories of heuristic-based (Schneider et al., 2011; Chan & Akoglu, 2016; Yazıcıoglu et al., 2015; Rong & Liu, 2018) and evolutionary computation (Zhou & Liu, 2014) . These methods improve the resilience of complex networks by minimally modifying graph topologies based on a degree-preserving atomic operation called edge rewiring (Schneider et al., 2011; Chan & Akoglu, 2016; Rong & Liu, 2018) . Concretely, for a given graph G = (V, E) and two existing edges AC and BD, an edge rewiring operation alters the graph structure by removing AC and BD and adding AB and CD, where AC, BD ∈ E and AB, CD, AD, BC / ∈ E. Edge rewiring has some nice properties against simply addition or deletion of edges: 1) it preserves node degree, while addition may violate capacity constraints; 2) it achieves minimal utility degradation in terms of graph Laplacian measurement, while addition/deletion may lead to a large network utility degradation (Jaume et al., 2020; Ma et al., 2021) . Despite their success, learning-free methods share the following limitations:



In this paper, network resilience and network resilience are used interchangeably.1

