A clarified typology of core-periphery structure in networks

Gallagher, Ryan J.; Young, Jean-Gabriel; Welles, Brooke Foucault

doi:10.1126/sciadv.abc9800

Cited by 57 publications

(24 citation statements)

References 43 publications

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“…The concept of a network core-periphery structure was formalized and studied by Borgatti and Everett [4]. As mentioned in this work, and also noted by many subsequent authors [10,11,15], there are several different types of core-periphery structure, and hence detection algorithm, that can be defined. First, we may distinguish between partitions [5,14,32] that map nodes into two sets, the core and the periphery, and orderings [11,21,28,29] that assign a nonnegative "coreness" score to each node.…”

Section: Related Workmentioning

confidence: 86%

“…Figure 1 illustrates the difference between (2) and (3). Here the networks are samples of a stochastic block model [11,15,28,30,32]. We will let SBM(N, M, p 1 , p 2 , p 3 ) denote the stochastic block model with N nodes, a core of size M and core-core, core-periphery and periphery-periphery probabilities of p 1 , p 2 and p 3 , respectively.…”

Section: Objective Functionmentioning

confidence: 99%

“…The latter are closely associated with node centrality measures [20], and, of course, a continuous score can be used for subsequent ranking and partitioning. Second, while there is general consistency around the principle that core nodes should be well-connected and peripheral nodes should be poorly connected, there is a choice to be made about whether edges that join a core node and a peripheral node should occur with high/intermediate frequency [11,27,30,32] or low frequency [15], or whether such edges are irrelevant [5,14,20].…”

Section: Related Workmentioning

confidence: 99%

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Testing a QUBO Formulation of Core-periphery Partitioning on a Quantum Annealer

Higham¹,

Higham²,

Tudisco³

2022

Preprint

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We propose a new kernel that quantifies success for the task of computing a coreperiphery partition for an undirected network. Finding the associated optimal partitioning may be expressed in the form of a quadratic unconstrained binary optimization (QUBO) problem, to which a state-of-the-art quantum annealer may be applied. We therefore make use of the new objective function to (a) judge the performance of a quantum annealer, and (b) compare this approach with existing heuristic core-periphery partitioning methods. The quantum annealing is performed on the commercially available D-Wave machine. The QUBO problem involves a full matrix even when the underlying network is sparse. Hence, we develop and test a sparsified version of the original QUBO which increases the available problem dimension for the quantum annealer. Results are provided on both synthetic and real data sets, and we conclude that the QUBO/quantum annealing approach offers benefits in terms of optimizing this new quantity of interest. MotivationClustering, or community detection, is a fundamental tool for extracting high-level information from a network [13]. However, it is now widely acknowledged that quantifying and discovering other forms of meso-scale structure may also reveal useful insights. In this work we look at the issue of identifying core-periphery structure; we seek a set of nodes that are highly connected both internally and with the rest of the network, forming the core, and a set of peripheral nodes that are well connected to the core but have only sparse internal connections. This type of core-periphery structure has been observed to arise naturally in a number of settings, including protein interaction, cell signalling, gene regulation, ecology, social interaction and global trade; see, for example, [10] for a review. Further, as pointed out in [3], the structure may arise as a consequence of the data collection process. For example, a phone service provider may only have access to calls in which at least one of the participants is a customer; so there will be no record of calls between pairs of non-customers, who thus inhabit the periphery. We are concerned in this work with the "inverse problem" where a set of nodes and (undirected, unweighted) edges are supplied, and the task is to partition the nodes into a core and periphery; this may provide useful information about the roles of individual nodes and may also lead to more instructive visualizations [4,10,32].

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Section: Related Workmentioning

confidence: 86%

Section: Objective Functionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Testing a QUBO Formulation of Core-periphery Partitioning on a Quantum Annealer

Higham¹,

Higham²,

Tudisco³

2022

Preprint

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“…The other Bayesian method that we describe is from Gallagher et al (2021). Their likelihood is the same as that of Snijders and Nowicki (1997) and Zhang et al (2015) but they give extra attention to the prior on the block probabilities by explicitly enforcing the CP condition into the prior.…”

Section: Bayesianmentioning

confidence: 99%

Core-periphery structure in networks: a statistical exposition

Yanchenko¹,

Sengupta²

2022

Preprint

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Many real-world networks are theorized to have core-periphery structure consisting of a densely-connected core and a loosely-connected periphery. While this network feature has been extensively studied in various scientific disciplines, it has not received sufficient attention in the statistics community. In this expository article, our goal is to raise awareness about this topic and encourage statisticians to address the many interesting open problems in this area. We present the current research landscape by reviewing the most popular metrics and models that have been used for quantitative studies on core-periphery structure. Next, we formulate and explore various inferential problems in this context, such as estimation, hypothesis testing, and Bayesian inference, and discuss related computational techniques. We also outline the multidisciplinary scientific impact of core-periphery structure in a number of real-world networks. Throughout the article, we provide our own interpretation of the literature from a statistical perspective, with the goal of prioritizing open problems where contribution from the statistics community will be effective and important.

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“…An important feature of our heuristic policy is that the nodes with large degrees tend to form larger facets, resulting in a core-periphery structure [41] with dangling and isolated facets on the fringe. Therefore, the heuristic tends to find a realization with a maximized number of connected components (large β 0 ) and a minimized number of loops (small β 1 ).…”

Section: Rule 3 (Formentioning

confidence: 99%

Construction of simplicial complexes with prescribed degree-size sequences

Yen

2021

Preprint

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We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s ≥ 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

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A clarified typology of core-periphery structure in networks

Cited by 57 publications

References 43 publications

Testing a QUBO Formulation of Core-periphery Partitioning on a Quantum Annealer

Testing a QUBO Formulation of Core-periphery Partitioning on a Quantum Annealer

Core-periphery structure in networks: a statistical exposition

Construction of simplicial complexes with prescribed degree-size sequences

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