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Many complex networks expose global hub structures: for some nodes, the number of incident edges far exceeds the average, leading to a small average shortest path length. Such ‘small-world properties’ are often guided by a scale-free power-law distribution of the node degrees, and self-organization inside the network has been identified as a reason driving the emergence of this structure. Small-world networks have recently raised lots of interest, because they capture the global topology of the World-Wide Web, metabolic, and social networks. While small-world networks reflect global structures, little attention is paid to the local structure of complex networks. In this article neighbourhoods are demonstrated to share a common local structure in many real complex networks, manifested by a polynomial volume law. This law can, in case of networks that are embedded in space, be explained in terms of the …