Network isolators inhibit failure spreading in complex networks

Franz Kaiser,Vito Latora,Dirk Witthaut

doi:10.1038/s41467-021-23292-9

Abstract

In our daily lives, we rely on the proper functioning of supply networks, from power grids to water transmission systems. A single failure in these critical infrastructures can lead to a complete collapse through a cascading failure mechanism. Counteracting strategies are thus heavily sought after. In this article, we introduce a general framework to analyse the spreading of failures in complex networks and demostrate that not only decreasing but also increasing the connectivity of the network can be an effective method to contain damages. We rigorously prove the existence of certain subgraphs, called network isolators, that can completely inhibit any failure spreading, and we show how to create such isolators in synthetic and real-world networks. The addition of selected links can thus prevent large scale outages as demonstrated for power transmission grids.

Highlights

In our daily lives, we rely on the proper functioning of supply networks, from power grids to water transmission systems
Consider a simple graph G with edge set E and vertex set V consisting of L = ∣E∣ edges and N = ∣V∣ vertices. Many such systems can be modelled by linear flow networks where the flow over an edge e = (i, j) 2 E(G) depends linearly on the gradient of a potential function across the edge, Fi!j 1⁄4 Aij Á ðθi À θjÞ: ð1Þ. This description applies to power transmission grids[2,24,25,26], where F is the real power flow, θi denotes the nodal voltage phase angle and Aij is given by the line susceptance
Since most real world examples of networks do not contain perfect network isolators, we have studied the robustness of a network isolator against modifications of the topology

Summary

Introduction

We rely on the proper functioning of supply networks, from power grids to water transmission systems. We introduce a general framework to analyse the spreading of failures in complex networks and demostrate that decreasing and increasing the connectivity of the network can be an effective method to contain damages. The response to an edge failure is strong locally, but it is reduced in the other module of the network which has only few links connecting to the part where the failure happened. An exceptionally strong interconnectivity between two modules can suppress failure spreading as shown, e. In real vascular networks of leaves the suppression of failure spreading occurs naturally because the central vein between the left and right parts has an exceptionally large weight (Fig. 1e, cf [23])

Methods

Results

Conclusion