The network metaphor in the analysis of urban and territorial cases has a long tradition especially in transportation/land-use planning and economic geography. More recently, urban design has brought its contribution by means of the "space syntax" methodology. All these approaches -though under different terms like "accessibility", "proximity", "integration" "connectivity", "cost" or "effort" -focus on the idea that some places (or streets) are more important than others because they are more central. The study of centrality in complex systems, however, originated in other scientific areas, namely in structural sociology, well before its use in urban studies; moreover, as a structural property of the system, centrality has never been extensively investigated metrically in geographic networks as it has been topologically in a wide range of other relational networks like social, biological or technological.After two previous works on some structural properties of the dual and primal graph representations of urban street networks (Porta et al. 2004;Crucitti et al. 2005), in this paper we provide an in-depth investigation of centrality in the primal approach as compared to the dual one, with a special focus on potentials for urban design. An innovative methodology for the analysis of geographic spatial networks, which we term Multiple Centrality Assessment (MCA), is defined and experimented on four real urban street systems. MCA, it turns out, provides a new perspective to the network analysis of spatial systems, which is inherently different from space syntax in that: 1. it is based on a primal, rather than a dual, graph representation of street patterns; 2. it works within a fully metric, rather than topologic, framework; 3. it investigates a set of peer centrality indices rather than just a principal one. We show that spatially, some centrality indices nicely capture the "skeleton" of the urban structure that so much impacts on spatial cognition and collective behaviors; we also show that statistically, centrality distributions consistently characterize geographically different patterns, and power laws emerge in self-organized cities.