  This paper aims to measure the efficiency of urban street networks (a kind of
complex networks) from the perspective of the multidimensional chain of
connectivity (or flow). More specifically, we define two quantities: flow
dimension and flow capacity, to characterize structures of urban street
networks. To our surprise for the topologies of urban street networks,
previously confirmed as a form of small world and scale-free networks, we find
that (1) the range of their flow dimension is rather wider than their random
and regular counterparts, (2) their flow dimension shows a power-law
distribution, and (3) they have a higher flow capacity than their random and
regular counterparts. The findings confirm that (1) both the wider range of
flow dimension and the higher flow capacity can be a signature of small world
networks, and (2) the flow capacity can be an alternative quantity for
measuring the efficiency of networks or that of the individual nodes. The
findings are illustrated using three urban street networks (two in the Europe
and one in the USA).
