Random Spatial Network Models for Core-Periphery Structure

Abstract

Core-periphery structure is a common property of complex networks, which is a composition of tightly connected groups of core vertices and sparsely connected periphery vertices. This structure frequently emerges in traffic systems, biology, and social networks via underlying spatial positioning of the vertices. While core-periphery structure is ubiquitous, there have been limited attempts at modeling network data with this structure. Here, we develop a generative, random network model with core-periphery structure that jointly accounts for topological and spatial information by "core scores" of vertices. Our model achieves substantially higher likelihood than existing generative models of core-periphery structure, and we demonstrate how the core scores can be used in downstream data mining tasks, such as predicting airline traffic and classifying fungal networks. We also develop nearly linear time algorithms for learning model parameters and network sampling by using a method akin to the fast multipole method, a technique traditional to computational physics, which allow us to scale to networks with millions of vertices with minor tradeoffs in accuracy.Networks are widely used to model the interacting components of complex systems emerging from biology, ecosystems, economics, and sociology [1][2][3]. A typical network consists of a set of vertices V and a set of edges E, where the vertices represent discrete objects (e.g., people or cities) and the edges represent pairwise connections (e.g., friendships or highways). Networks are often described in terms of local properties such as vertex degree or local clustering coefficients and global properties such as diameter or the number of connected components. At the same time, a number of mesoscale proprieties are consistently observed in real-world networks, which often reveal important structural information of the underlying complex systems; arguably the most well-known is community structure, and a tremendous amount of effort has been devoted to its explanation and algorithmic identification [4][5][6][7].

Sublinear domination and core–periphery networks

“…Avin et al present an axiomatic approach towards core-periphery networks and draw strong conclusions [6]. Generative models for core-periphery networks have also been studied at [3,[7][8][9]. The closest model to ours is the stochastic blockmodel of [3] which assumes that core-core nodes are connected with probability p CC , periphery-periphery nodes are connected with probability p P P and coreperiphery nodes are connected with probability p CP , with p CC > p CP > p P P , and its recent extension to directed graphs in [9].…”

A Nonlinear Spectral Method for Core--Periphery Detection in Networks

“…We see that, relative to the Heaviside version, this model gives a smoother transition from core to periphery, and has a built-in notion of ranking within each group. The relevance of this model to capture core and perhipheral nodes has been also recently pointed out in [21].…”

Stochastic Opinion Dynamics for Interest Prediction in Social Networks

“…However, they do not provide an algorithm for efficiently identifying the core in large networks, as we do in this work. Finally, the work of [50] is close to ours as it proposes a generative model for core-periphery networks that exhibits a core of sublinear size (wrt to the size of the network) that acts as an almost dominating set of the network, fits the model to real-world small-scale networks, and compares with [32,61].…”

“…Most modern large-scale Online Social Networks (OSN) exhibit the so-called core-periphery structure (see e.g., [32,47,50,51,57,62,65,65] and the references therein). Namely, their nodes are naturally partitioned into a core set of nodes tightly connected with each other, and a periphery set , where the nodes are sparsely connected, but are relatively well-connected to the core.…”