  A new measure $c(e)$ of the centrality of an edge $e$ in an undirected graph
$G$ is introduced. It is based on the variation of the Kemeny constant of the
graph after removing the edge $e$. The new measure is designed in such a way
that the Braess paradox is avoided. A numerical method for computing $c(e)$ is
introduced and a regularization technique is designed in order to deal with
cut-edges and disconnected graphs. Numerical experiments performed on synthetic
tests and on real road networks show that this measure is particularly
effective in revealing bottleneck roads whose removal would greatly reduce the
connectivity of the network.
