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How to Calculate the Barycenter of a Weighted Graph

Author

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  • Sébastien Gadat

    (Toulouse School of Economics, Université Toulouse 1 Capitole, 31042 Toulouse, France)

  • Ioana Gavra

    (Institut de Mathématiques de Toulouse, Université Toulouse 3 Paul Sabatier, 31400 Toulouse, France)

  • Laurent Risser

    (Institut de Mathématiques de Toulouse, CNRS, 31400 Toulouse, France)

Abstract

Discrete structures like graphs make it possible to naturally and flexibly model complex phenomena. Since graphs that represent various types of information are increasingly available today, their analysis has become a popular subject of research. Yet, even an algorithm for locating the average position in graphs is lacking although this knowledge would be of primary interest for statistical analysis or representation problems. In this work, we develop a stochastic algorithm for finding the Fréchet mean of weighted undirected metric graphs. This method relies on a noisy simulated annealing algorithm dealt with using homogenization. We then illustrate our algorithm with three examples (subgraphs of a social network, subgraph of a collaboration and citation network, and a transport network).

Suggested Citation

  • Sébastien Gadat & Ioana Gavra & Laurent Risser, 2018. "How to Calculate the Barycenter of a Weighted Graph," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1085-1118, November.
    • Handle: RePEc:inm:ormoor:v:43:y:2018:i:4:p:1085-1118
    DOI: 10.1287/moor.2017.0896
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    References listed on IDEAS

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    1. Hakimi, S. Louis, 1983. "On locating new facilities in a competitive environment," European Journal of Operational Research, Elsevier, vol. 12(1), pages 29-35, January.
    2. Daron Acemoğlu & Giacomo Como & Fabio Fagnani & Asuman Ozdaglar, 2013. "Opinion Fluctuations and Disagreement in Social Networks," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 1-27, February.
    3. Olga Klopp & Alexandre Tsybakov & Nicolas Verzelen, 2016. "Oracle inequalities for network models and sparse graphon estimation," Working Papers 2016-13, Center for Research in Economics and Statistics.
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    Cited by:

    1. Crespo, Marelys & Gadat, Sébastien & Gendre, Xavier, 2023. "Stochastic Langevin Monte Carlo for (weakly) log-concave posterior distributions," TSE Working Papers 23-1398, Toulouse School of Economics (TSE).
    2. Steffen Borgwardt, 2022. "An LP-based, strongly-polynomial 2-approximation algorithm for sparse Wasserstein barycenters," Operational Research, Springer, vol. 22(2), pages 1511-1551, April.

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