  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. 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 Frechet 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).
