  In the stochastic exploration of geometrically embedded graphs, intuition
suggests that providing a shortcut between a pair of nodes reduces the mean
first passage time of the entire graph. Counterintuitively, we find a Braess
paradox analog. For regular diffusion, shortcuts can worsen the overall search
efficiency of the network, although they bridge topologically distant nodes. We
propose an optimization scheme under which each edge adapts its conductivity to
minimize the graph's search time. The optimization reveals a relationship
between the structure and diffusion exponent and a crossover from dense to
sparse graphs as the exponent increases.
