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Core-periphery models via integer programming: maximizing the influence of the core

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Abstract

Core-periphery models are a commonly used and powerful tool in network analysis which allow researchers to identify a set of highly influential members (the core) based on the structure of the network. However, there is no standard method for core identification. Worse yet, for researchers in fields such as economics, existing methods often do not allow for researchers to make meaningful inferences from core-periphery analyses. This paper introduces a new method using integer programming to identify the core of a weighted network with either symmetric or asymmetric relationships and without the aid of any a priori assumptions. The integer program maximizes the weighted influence of the members of the core while imposing a set of user-parameterized connectivity constraints, both within the core and between the core and the periphery. As a result, this model generalizes previous concepts of the core of a network, i.e., an idealized core, through the flexibility created by the two connectivity parameters. These parameters give researchers the freedom to apply discipline specific theory to core-periphery analyses. This approach also offers drastically improved handling of directed data compared to existing methods of core-periphery analysis. An algorithm which converts the initially non-linear integer program into a linear integer programming approach is presented, and several examples are studied using this method to demonstrate its efficacy including a data set of international collaborations in academic publications and a data set of US railway shipments.

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Notes

  1. In graph theory, a subset X of the vertex set is said to dominate another subset Y of the vertex set if for every \(y\in Y\) there exists an \(x\in X\) such that xy is an edge in the network. Recall that in undirected networks the edge xy is the exact same thing as the edge yx, but in directed networks xy and yx are distinct objects.

  2. This is the idea behind the concept of continuous cores described in Borgatti and Everett (2000)

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Authors and Affiliations

  1. Division of Resource Economics and Management, West Virginia University, Morgantown, WV, USA

    Michael Cary

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  1. Michael Cary
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Correspondence to Michael Cary.

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Communicated by Leonardo de Lima.

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Cary, M. Core-periphery models via integer programming: maximizing the influence of the core. Comp. Appl. Math. 42, 162 (2023). https://doi.org/10.1007/s40314-023-02299-6

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  • DOI: https://doi.org/10.1007/s40314-023-02299-6

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