A graph G is a Helly graph if for any pairwise intersecting set of
balls, there exists a vertex belonging to all these balls (i.e., the
family of balls of G satisfy the Helly property). This class of
graphs is a large class and for every graph G, there exists a
"smallest" Helly graph H in which G embeds isometrically.
In this talk, I will present a "local-to-global" characterization of
these graphs: a graph G is Helly if and only if the cliques of G
satisfy the Helly property and if the clique complex of G is simply
connected.