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Centrality measures in networks

Author

Listed:
  • Francis Bloch

    (Université Paris 1 and Paris School of Economics)

  • Matthew O. Jackson

    (Stanford University, External Faculty of the Santa Fe Institute)

  • Pietro Tebaldi

    (Columbia University and NBER)

Abstract

We show that prominent centrality measures in network analysis are all based on additively separable and linear treatments of statistics that capture a node’s position in the network. This enables us to provide a taxonomy of centrality measures that distills them to varying on two dimensions: (i) which information they make use of about nodes’ positions, and (ii) how that information is weighted as a function of distance from the node in question. The three sorts of information about nodes’ positions that are usually used—which we refer to as “nodal statistics”—are the paths from a given node to other nodes, the walks from a given node to other nodes, and the geodesics between other nodes that include a given node. Using such statistics on nodes’ positions, we also characterize the types of trees such that centrality measures all agree, and we also discuss the properties that identify some path-based centrality measures.

Suggested Citation

  • Francis Bloch & Matthew O. Jackson & Pietro Tebaldi, 2023. "Centrality measures in networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 413-453, August.
    • Handle: RePEc:spr:sochwe:v:61:y:2023:i:2:d:10.1007_s00355-023-01456-4
    DOI: 10.1007/s00355-023-01456-4
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    3. Yan Leng & Xiaowen Dong & Esteban Moro & Alex Pentland, 2024. "Long-Range Social Influence in Phone Communication Networks on Offline Adoption Decisions," Information Systems Research, INFORMS, vol. 35(1), pages 318-338, March.

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