2021
DOI: 10.1098/rspa.2021.0026
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Dimension-reduction of dynamics on real-world networks with symmetry

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-s… Show more

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Cited by 4 publications
(4 citation statements)
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“…The first approach involves comparing the topology of different networks as an outcome of other network properties (e.g., network size). This is common in network science where understanding the generative processes underlying network formation is a major focus (e.g., Ojer & Pastor-Satorras, 2022;Rocha et al, 2021;Ward, 2021). However, it is also of interest to ecologists, such as with studies that test the relationship between network size and modularity (Griffin & Nunn, 2012).…”
Section: Comparisons Of Network Propertiesmentioning
confidence: 99%
See 1 more Smart Citation
“…The first approach involves comparing the topology of different networks as an outcome of other network properties (e.g., network size). This is common in network science where understanding the generative processes underlying network formation is a major focus (e.g., Ojer & Pastor-Satorras, 2022;Rocha et al, 2021;Ward, 2021). However, it is also of interest to ecologists, such as with studies that test the relationship between network size and modularity (Griffin & Nunn, 2012).…”
Section: Comparisons Of Network Propertiesmentioning
confidence: 99%
“…Several studies (6/49 = 12%) used animal social network meta‐datasets to illustrate new methods or confirm trends in network science or related fields. These included identifying novel scaling trends (Ojer & Pastor‐Satorras, 2022; Rocha et al., 2021; Ward, 2021), producing new approaches (McDonald & Hobson, 2018; Ojer & Pastor‐Satorras, 2022; Shizuka & Farine, 2016; Ward, 2021) or deriving new network traits (Péron, 2023).…”
Section: The Current State Of Comparative Network Analysismentioning
confidence: 99%
“…These included identifying novel scaling trends (Rocha et al 2021;Ward 2021;Ojer & Pastor-Satorras 2022), producing new approaches (Shizuka & Farine 2016;McDonald & Hobson 2018;Ward 2021;Ojer & Pastor-Satorras 2022), or deriving new network traits (Péron 2023).…”
Section: The Current State Of Comparative Network Analysismentioning
confidence: 99%
“…This is common in network science where understanding the generative processes underlying network formation is a major focus (e.g. (Rocha et al 2021;Ward 2021;Ojer & Pastor-Satorras 2022)).…”
Section: Box 2: Classifying Comparative Network Analysesmentioning
confidence: 99%