It may surprise you, but you might consider algebraic topology. See Maurice Herlihy's marvellous little book, Distributed Computing through Combinatorial Topol

It may surprise you, but you might consider algebraic topology. See Maurice Herlihy's marvellous little book, Distributed Computing through Combinatorial Topology. The idea is that the state of a distributed computation can be represented as a simplicial complex (think "graph" only in higher dimensions), and that steps in a protocol correspond to continuous transformations applied to the complex. The result is that significant distributed computing problems get reduced to well-known results from combinatorial topology, and they "just fall out".