  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.

Dynamical Systems