Finding multiple core-periphery pairs in networks

Abstract

With a core-periphery structure of networks, core nodes are densely interconnected, peripheral nodes are connected to core nodes to different extents, and peripheral nodes are sparsely interconnected. Core-periphery structure composed of a single core and periphery has been identified for various networks. However, analogous to the observation that many empirical networks are composed of densely interconnected groups of nodes, i.e., communities, a network may be better regarded as a collection of multiple cores and peripheries. We propose a scalable algorithm to detect multiple nonoverlapping groups of core-periphery structure in a network. We illustrate our algorithm using synthesized and empirical networks. For example, we find distinct core-periphery pairs with different political leanings in a network of political blogs and separation between international and domestic subnetworks of airports in some single countries in a worldwide airport network.

Revealing in-block nestedness: Detection and benchmarking

“…Along this line, the door remains open to further development. For example, slight modifications on our formulation generalize the notion of multiple core-periphery structures, which has been recently addressed from a different starting point [43]. Other directions may be related to identification techniques (e.g., stochastic block models [44]) or the design of distinct, specialized null models [45,46].…”

Core-periphery structure requires something else in the network

“…A core-periphery structure in its simplest form refers to a partition of a network into two groups of nodes called core and periphery, where core nodes are densely interconnected (i.e., adjacent), and peripheral nodes are adjacent to the core nodes but not to other peripheral nodes [8][9][10]. Core-periphery structure has been detected in a number of networks including social networks [8,[10][11][12][13][14][15][16][17][18][19][20], protein-protein interaction networks [15,21,22], neural networks [23,24], trade networks [13,25,26], financial networks [14,[27][28][29][30][31] and transportation networks [10,13,14,19,32]. For example, in a world-trade network among countries, economically strong countries trade with other strong countries, constituting a core.…”

“…To solve the conundrum that one does not discover core-periphery structure using the configuration model as the null model, we propose that one must add at least one different block apart from a core block and the corresponding periphery block for a network to have core-periphery structure that is consistent with figure 1. Such blocks may be a community, sparsely connected part, a different core-periphery pair [10,19,20,32], a core that shares the periphery with the focal core-periphery pair [34] and so forth. Then, we propose a scalable algorithm to partition a network into multiple core-periphery pairs including community detection as special cases, aiming to detect core-periphery structure that is not merely explained by the degree of each node.…”

Network models of financial systemic risk: a review

“…This suggests that even if there were no such a standard core-periphery structure in the empirical network, the estimation method classifies each node as either a core node or a peripheral node. In fact, recent studies argue that the seemingly core-periphery structure might just come from a heterogeneous degree distribution or consist of two cores [88][89][90]. As an example, visualization of Italian interbank networks aggregated over 10 business days is presented in Fig.…”

“…However, in 2007, Italian banks and other foreign banks seem to form two core-like groups, which would make it difficult to extract a stylized pure core-periphery structure. It might be reasonable to infer that there are two core-periphery structures in the network [89].…”