Extreme vulnerability to intruder attacks destabilizes network dynamics

TL;DR

This paper reveals that a single intruder node can destabilize complex networks more efficiently than multiple attackers, especially when targeting low-degree nodes, challenging previous assumptions about network vulnerability.

Contribution

It introduces a new vulnerability characterization showing low-degree nodes are more critical targets than hubs, and provides scaling laws for network susceptibility to attacks.

Findings

Single adversarial nodes can destabilize entire networks.

Targeting low-degree nodes induces greater instability than hubs.

Larger networks are less susceptible to single-node attacks.

Abstract

Consensus, synchronization, formation control, and power grid balance are all examples of virtuous dynamical states that may arise in networks. Here, we focus on how such states can be destabilized from a fundamental perspective; namely, we address the question of how one or a few intruder agents within an otherwise functioning network may compromise its dynamics. We show that a single adversarial node coupled via adversarial connections to one or more other nodes is sufficient to destabilize the entire network, which we prove to be more efficient than targeting multiple nodes. Then, we show that concentrating the attack on a single low-degree node induces the greatest instability, challenging the common assumption that hubs are the most critical nodes. This leads to a new characterization of the vulnerability of a node, which contrasts with previous work, and identifies low-indegree nodes (as opposed to the hubs) as the most vulnerable components of a network. Our results are derived for linear systems but hold true for nonlinear networks, including those described by the Kuramoto model. Finally, we derive scaling laws showing that larger networks are less susceptible, on average, to single-node attacks. Overall, these findings highlight an intrinsic vulnerability of technological systems, such as autonomous networks, sensor networks, power grids, and the Internet of Things, with implications that extend also to the realm of complex social and biological networks.