title: Density-based and transport-based core-periphery structures in networks.
abstract: Networks often possess mesoscale structures, and studying them can yield insights into both structure and function. It is most common to study community structure, but numerous other types of mesoscale structures also exist. In this paper, we examine core-periphery structures based on both density and transport. In such structures, core network components are well-connected both among themselves and to peripheral components, which are not well-connected to anything. We examine core-periphery structures in a wide range of examples of transportation, social, and financial networks-including road networks in large urban areas, a rabbit warren, a dolphin social network, a European interbank network, and a migration network between counties in the United States. We illustrate that a recently developed transport-based notion of node coreness is very useful for characterizing transportation networks. We also generalize this notion to examine core versus peripheral edges, and we show that the resulting diagnostic is also useful for transportation networks. To examine the properties of transportation networks further, we develop a family of generative models of roadlike networks. We illustrate the effect of the dimensionality of the embedding space on transportation networks, and we demonstrate that the correlations between different measures of coreness can be very different for different types of networks.
authors.affiliation: Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
authors.forename: Sang Hoon
authors.initials: SH
authors.lastname: Lee
authors.affiliation: Program in Applied and Computational Mathematics (PACM), Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000, USA and Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095, USA.
authors.forename: Mihai
authors.initials: M
authors.lastname: Cucuringu
authors.affiliation: Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom and CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, United Kingdom.
authors.forename: Mason A
authors.initials: MA
authors.lastname: Porter