Affiliation:
1. School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
Abstract
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
10
7
, but the largest compression ratio identified is nearly
10
12
. 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.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献