Higher-order structure and epidemic dynamics in clustered networks.
Clustering is typically measured by the ratio of triangles to all triples regardless of whether open or closed. Generating clustered networks, and how clustering affects dynamics on networks, is reasonably well understood for certain classes of networks (Volz et al., 2011; Karrer and Newman, 2010), e.g. networks composed of lines and non-overlapping triangles. In this paper we show that it is possible to generate networks which, despite having the same degree distribution and equal clustering, exhibit different higher-order structure, specifically, overlapping triangles and other order-four (a closed network motif composed of four nodes) structures. To distinguish and quantify these additional structural features, we develop a new network metric capable of measuring order-four structure which, when used alongside traditional network metrics, allows us to more accurately describe a network׳s topology. Three network generation algorithms are considered: a modified configuration model and two rewiring algorithms. By generating homogeneous networks with equal clustering we study and quantify their structural differences, and using SIS (Susceptible-Infected-Susceptible) and SIR (Susceptible-Infected-Recovered) dynamics we investigate computationally how differences in higher-order structure impact on epidemic threshold, final epidemic or prevalence levels and time evolution of epidemics. Our results suggest that characterising and measuring higher-order network structure is needed to advance our understanding of the impact of network topology on dynamics unfolding on the networks.
School of Mathematical and Physical Sciences, Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK.
Martin
M
Ritchie
Centre for Computational Neuroscience and Robotics, University of Sussex, Falmer, Brighton BN1 9QH, UK; Institute of Child Health, University College London, London WC1E 6BT, UK.
Luc
L
Berthouze
Warwick Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK.
Thomas
T
House
School of Mathematical and Physical Sciences, Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK. Electronic address: i.z.kiss@sussex.ac.uk.
Istvan Z
IZ
Kiss
D016000:Cluster Analysis; D003141:Communicable Diseases / Q000453:epidemiology*; D058872:Epidemics; D006801:Humans; D008954:Models, Biological; D016571:Neural Networks, Computer
Clustering; Epidemic; Loops; Motif counting; Networks