Logistic growth on networks: exact solutions for the SI model
Abstract
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 manybody quantum systems. This allows us to organize the timedependent 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 MonteCarlo simulations, visibly departs from the meanfield results.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.03530
 Bibcode:
 2021arXiv210903530M
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Computer Science  Social and Information Networks;
 Physics  Physics and Society;
 Quantitative Biology  Populations and Evolution
 EPrint:
 6(+11) pages, 2(+1) figures, accompanied by a software package at https://doi.org/10.6084/m9.figshare.14872182.v3