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).
metric graphs; Markov process; simulated annealing; homogeneization;
Sébastien Gadat, Ioana Gavra, and Laurent Risser, “How to calculate the barycenter of a weighted graph”, TSE Working Paper, n. 16-652, May 2016.
Sébastien Gadat, Ioana Gavra, and Laurent Risser, “How to calculate the barycenter of a weighted graph”, Mathematics of Operations Research, vol. 43, n. 4, November 2018, pp. 1051–1404.
Mathematics of Operations Research, vol. 43, n. 4, November 2018, pp. 1051–1404