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

Logistic growth on networks: exact solutions for the SI model