Vulnerability Analysis for Complex Networks Using Aggressive Abstraction

TL;DR

This paper introduces a scalable method for analyzing vulnerabilities in complex networks by creating simplified, mathematically equivalent abstractions and applying formal analysis techniques, demonstrated on power grid, biological, and social networks.

Contribution

It develops a novel approach combining finite state abstractions with formal analysis to efficiently identify vulnerabilities in large, complex networks.

Findings

Efficient algorithms for vulnerability-preserving abstractions

Successful case study on a realistic power grid model

Applicability to biological and social networks

Abstract

Large, complex networks are ubiquitous in nature and society, and there is great interest in developing rigorous, scalable methods for identifying and characterizing their vulnerabilities. This paper presents an approach for analyzing the dynamics of complex networks in which the network of interest is first abstracted to a much simpler, but mathematically equivalent, representation, the required analysis is performed on the abstraction, and analytic conclusions are then mapped back to the original network and interpreted there. We begin by identifying a broad and important class of complex networks which admit vulnerability-preserving, finite state abstractions, and develop efficient algorithms for computing these abstractions. We then propose a vulnerability analysis methodology which combines these finite state abstractions with formal analytics from theoretical computer science to yield a comprehensive vulnerability analysis process for networks of realworld scale and complexity. The potential of the proposed approach is illustrated with a case study involving a realistic electric power grid model and also with brief discussions of biological and social network examples.