How to calculate the barycenter of a weighted graph

Sébastien Gadat (), Ioana Gavra and Laurent Risser

No 16-652, TSE Working Papers from Toulouse School of Economics (TSE)

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).

Keywords: metric graphs; Markov process; simulated annealing; homogeneization (search for similar items in EconPapers)
Date: 2016-05
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Related works:
Journal Article: How to Calculate the Barycenter of a Weighted Graph (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:30480

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