  The SI model is the most basic of all compartmental models used to describe
the spreading of information through a population. Despite its apparent
simplicity, the analytic solution of this model on networks is still lacking.
We address this problem here, using a novel formulation inspired by the
mathematical treatment of many-body quantum systems. This allows us to organize
the time-dependent expectation values for the state of individual nodes in
terms of contributions from subgraphs of the network. We compute these
contributions systematically and find a set of symmetry relations among
subgraphs of differing topologies. We use our novel approach to compute the
spreading of information on three different sample networks. The exact
solution, which matches with Monte-Carlo simulations, visibly departs from the
mean-field results.
