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We develop an analytical approach which provides the dependence of the meanfirst-passage time (MFPT) for random walks on complex networks both on thetarget connectivity and on the source-target distance. Our approach putsforward two strongly different behaviors depending on the type - compact or noncompact - of the random walk. In the case of non compact exploration, we showthat the MFPT scales linearly with the inverse connectivity of the target, andis largely independent of the starting point. On the contrary, in the compactcase the MFPT is controlled by the source-target distance, and we find thatunexpectedly the target connectivity becomes irrelevant for remote targets.

Close or connected? Distance and connectivity effects on transport in networks