title: Dynamics on modular networks with heterogeneous correlations.
abstract: We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module, and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and Lancichinetti-Fortunato-Radicchi networks) by allowing a heterogeneous distribution of degree-degree correlations across modules, which is important for the consideration of nonidentical interacting networks.
authors.affiliation: MACSI, Department of Mathematics & Statistics, University of Limerick, Ireland.
authors.forename: Sergey
authors.initials: S
authors.lastname: Melnik
authors.affiliation: Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
authors.forename: Mason A
authors.initials: MA
authors.lastname: Porter
authors.affiliation: Department of Mathematics, Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250, USA.
authors.forename: Peter J
authors.initials: PJ
authors.lastname: Mucha
authors.affiliation: MACSI, Department of Mathematics & Statistics, University of Limerick, Ireland.
authors.forename: James P
authors.initials: JP
authors.lastname: Gleeson
mesh_terms: D000465:Algorithms; D020407:Internet; D008962:Models, Theoretical; D060066:Protein Interaction Maps; D012944:Social Support; D013997:Time Factors; D014495:Universities