  To characterize the location (mean, median) of a set of graphs, one needs a
notion of centrality that is adapted to metric spaces, since graph sets are not
Euclidean spaces. A standard approach is to consider the Fr\'echet mean. In
this work, we equip a set of graph with the pseudometric defined by the
$\ell_2$ norm between the eigenvalues of their respective adjacency matrix .
Unlike the edit distance, this pseudometric reveals structural changes at
multiple scales, and is well adapted to studying various statistical problems
on sets of graphs. We describe an algorithm to compute an approximation to the
Fr\'echet mean of a set of undirected unweighted graphs with a fixed size.
