  For a given, arbitrary graph, what is the epidemic threshold? That is, under
what conditions will a virus result in an epidemic? We provide the super-model
theorem, which generalizes older results in two important, orthogonal
dimensions. The theorem shows that (a) for a wide range of virus propagation
models (VPM) that include all virus propagation models in standard literature
(say, [8][5]), and (b) for any contact graph, the answer always depends on the
first eigenvalue of the connectivity matrix. We give the proof of the theorem,
arithmetic examples for popular VPMs, like flu (SIS), mumps (SIR), SIRS and
more. We also show the implications of our discovery: easy (although sometimes
counter-intuitive) answers to `what-if' questions; easier design and evaluation
of immunization policies, and significantly faster agent-based simulations.
