Multicores-periphery structure in networks
📝 Abstract
Many real-world networks exhibit a multicores-periphery structure, with densely connected vertices in multiple cores surrounded by a general periphery of sparsely connected vertices. Identification of the multicores-periphery structure can provide a new lens to understand the structures and functions of various real-world networks. This paper defines the multicores-periphery structure and introduces an algorithm to identify the optimal partition of multiple cores and the periphery in general networks. We demonstrate the performance of our algorithm by applying it to a well-known social network and a patent technology network, which are best characterized by the multicores-periphery structure. The analyses also reveal the differences between our multicores-periphery detection algorithm and two state-of-the-art algorithms for detecting the single core-periphery structure and community structure.
💡 Analysis
Many real-world networks exhibit a multicores-periphery structure, with densely connected vertices in multiple cores surrounded by a general periphery of sparsely connected vertices. Identification of the multicores-periphery structure can provide a new lens to understand the structures and functions of various real-world networks. This paper defines the multicores-periphery structure and introduces an algorithm to identify the optimal partition of multiple cores and the periphery in general networks. We demonstrate the performance of our algorithm by applying it to a well-known social network and a patent technology network, which are best characterized by the multicores-periphery structure. The analyses also reveal the differences between our multicores-periphery detection algorithm and two state-of-the-art algorithms for detecting the single core-periphery structure and community structure.
📄 Content
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Multicores-periphery structure in networks
Bowen Yan and Jianxi Luo
Engineering Product Development Pillar and SUTD-MIT International Design Centre,
Singapore University of Technology and Design, Singapore, 487372
(bowen_yan@sutd.edu.sg and luo@sutd.edu.sg)
Abstract Many real-world networks exhibit a multicores-periphery structure, with densely connected vertices in multiple cores surrounded by a general periphery of sparsely connected vertices. Identification of the multicores-periphery structure can provide a new lens to understand the structures and functions of various real-world networks. This paper defines the multicores- periphery structure and introduces an algorithm to identify the optimal partition of multiple cores and the periphery in general networks. We demonstrate the performance of our algorithm by applying it to a well-known social network and a patent technology network, which are best characterized by the multicores-periphery structure. The analyses also reveal the differences between our multicores-periphery detection algorithm and two state-of-the-art algorithms for detecting the single core-periphery structure and community structure.
Keywords: meso-scale structure, core-periphery structure, community detection
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1 Introduction
Many real-world systems can be represented as networks, for instance, social networks,
technological networks, information networks, and biological networks. In the past two
decades, various algorithms have been developed to explore the structures of real-world
networks, which may reveal the properties and functions of the respective networks
(Newman, 2003; Strogatz, 2001). A particular and popular strand of network analyses has
focused on detecting meso-scale structures, such as communities (or clusters) in networks.
Vertices in the same community are more cohesively connected to each other than those in
different communities (Fortunato, 2010).
The core-periphery structure is an alternative meso-scale structure that has been
discovered in many real-world networks, such as social networks, transportation networks
and the World Wide Web (Borgatti & Everett, 2000; Csermely et al., 2013; Rombach et al.,
2014). A network characterized by the core-periphery structure exhibits some sort of core, in
which vertices are densely connected, and a periphery, in which vertices are only sparsely
connected. Both community and core-periphery structures have important implications on the
functions in the networks that embed them (Zhang et al., 2015). For instance, in
communication networks, dense connections in a dense community or core may lead to
efficient information flow or synchronization among vertices in the same community or core
(Wasserman & Faust, 1994; Xu & Chen, 2005). In social networks, persons in the densely
connected core might be more influential or powerful than those in the periphery.
However, real-world networks can exhibit multiple cores, each of which contains vertices
that are only densely connected to each other within the respective cores, together with the
periphery, in which vertices are only sparsely connected in general. For example, in a social
network people may be cohesively connected in different sub-groups; meanwhile there are
always people who are only loosely connected to any of the sub-groups and other people in
general. A city may have multiple dense centers (i.e., cores) for different urban functions, and
a general sparse suburb (i.e., periphery) surrounding them. Rombach et al. (2014) observed
two cores in London’s underground railway network. Zhang et al. (Zhang et al., 2015)
visually identified two cores in the network of hyperlinks between political blogs, leaving
those generally loosely connected blogs in the periphery. In our earlier analysis of the
structure of a weighted network of patent technology classes that represent the total
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technology space (Yan & Luo, 2017), we vaguely observed several strong cores which
contain technology classes that are strongly and cohesively related to one another, and the
periphery consists of all outlying and weakly-connected technology classes.
These networks exhibit a meso-scale structure in common, i.e., multiple cores, each of
which contains densely connected vertices, surrounded by the periphery, which contains the
sparsely connected vertices. We refer to this structure as a “multicores-periphery structure”.
Figure 1 illustrates the fundamental differences between the newly defined multicores-
periphery structure and the well-known community and core-periphery structures. Moreover,
various studies have attempted to identify the periphery closely connected to a clique with a
maximum or required density, and resulted in a structure of multiple sets of dense cores and
their own affiliated peripheries (Bruckner et al., 2015; Everett & Borgatti, 2000; Yang &
Leskovec, 2014). The multic
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