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Dimension-reduction of dynamics on real-world networks with symmetry
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences  (IF2.704),  Pub Date : 2021-07-21, DOI: 10.1098/rspa.2021.0026
Jonathan A. Ward

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 of epidemics and voting behaviour, by exploiting redundancies due to symmetries. These formulae are applied in a large-scale study of such symmetry-induced lumping in real-world networks, from which we identify specific networks for which lumping enables exact analysis that could not have been done on the full state-space. For most networks, lumping gives a state-space compression ratio of up to 107, but the largest compression ratio identified is nearly 1012. Many of the highest compression ratios occur in animal social networks. We also present examples of types of symmetry found in real-world networks that have not been previously reported.