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How to calculate the barycenter of a weighted graph

Author

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  • Gadat, Sébastien
  • Gavra, Ioana
  • Risser, Laurent

Abstract

Discrete structures like graphs make it possible to naturally and exibly model complex phenomena. Since graphs that represent various types of information are increasingly available today, their analysis has become a popular subject of research. The graphs studied in the field of data science at this time generally have a large number of nodes that are not fairly weighted and connected to each other, translating a structural specification of the data. Yet, even an algorithm for locating the average position in graphs is lacking although this knowledge would be of primary interest for statistical 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 two examples (subgraphs of a social network and of a collaboration and citation network).

Suggested Citation

  • Gadat, Sébastien & Gavra, Ioana & Risser, Laurent, 2016. "How to calculate the barycenter of a weighted graph," TSE Working Papers 16-652, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:30480
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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. 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.
    3. 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.
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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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