We establish three criteria of hyperbolicity of a graph in terms of ``average
width of geodesic bigons''. In particular we prove that if the ratio of the Van
Kampen area of a geodesic bigon β and the length of β in the Cayley
graph of a finitely presented group G is bounded above then G is
hyperbolic.
We plan to use these results to characterize hyperbolic groups in terms of
random walks.Comment: 17 pages, 3 figure