Dimension-reduction of dynamics on real-world networks with symmetry

We derive explicit formulae to quantify the Markov chain state-space compression, or lumping, that can be achieved in a broad range of dynamical processes on real-world networks, including models epidemics and voting behaviour, by exploiting redundancies due symmetries. These are applied large-scale study such symmetry-induced lumping from which we identify specific networks for enables exact analysis could not have been done full state-space. For most gives compression ratio up 10 7 , but largest identified is nearly 12 . Many highest ratios occur animal social networks. also present examples types symmetry found previously reported.