Optimizing Graph Structure for Targeted Diffusion

TL;DR

This paper introduces a novel model and algorithm for optimizing network structures to enable targeted attacks while minimizing impact on the rest of the network, with applications in cybersecurity.

Contribution

The paper presents the POTION model and POTION-ALG algorithm, leveraging gradient methods and spectral theory for scalable targeted attack optimization.

Findings

Effective targeted attack optimization demonstrated on real networks.

A certification condition for subgraph immunity is proposed.

Algorithm scales well to large network datasets.

Abstract

The problem of diffusion control on networks has been extensively studied, with applications ranging from marketing to controlling infectious disease. However, in many applications, such as cybersecurity, an attacker may want to attack a targeted subgraph of a network, while limiting the impact on the rest of the network in order to remain undetected. We present a model POTION in which the principal aim is to optimize graph structure to achieve such targeted attacks. We propose an algorithm POTION-ALG for solving the model at scale, using a gradient-based approach that leverages Rayleigh quotients and pseudospectrum theory. In addition, we present a condition for certifying that a targeted subgraph is immune to such attacks. Finally, we demonstrate the effectiveness of our approach through experiments on real and synthetic networks.