Flow dimension and capacity for structuring urban street networks

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 dimensions 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 dimensions 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 Europe and one in the USA).