Sparse Networks with Core-Periphery Structure Cian Naik Department of Statistics, University of Oxford e-mail:
[email protected] Fran¸coisCaron Department of Statistics, University of Oxford e-mail:
[email protected] Judith Rousseau Department of Statistics, University of Oxford e-mail:
[email protected] Abstract: We propose a statistical model for graphs with a core-periphery structure. To do this we define a precise notion of what it means for a graph to have this structure, based on the sparsity properties of the subgraphs of core and periphery nodes. We present a class of sparse graphs with such properties, and provide methods to simulate from this class, and to perform posterior inference. We demonstrate that our model can detect core-periphery structure in simulated and real-world networks. MSC 2010 subject classifications: Primary 62F15, 05C80; secondary 60G55. Keywords and phrases: Bayesian Nonparametrics, Completely Random Measures, Poisson random measures, Networks, Random Graphs, Sparsity, Point Processes. 1. Introduction Network data arises in a number of areas, including social, biological and trans- port networks. Modelling of this type data has become an increasingly important field in recent times, partly due to the greater availability of the data, and also due to the fact that we increasingly want to model complex systems with many interacting components. A central topic within this field is the design of ran- dom graph models. Various models have been proposed, building on the early arXiv:1910.09679v1 [stat.ME] 21 Oct 2019 work of [12]. A key goal with these models is to capture important properties of real-world graphs.