Local assortativeness in scale-free networks

The level of assortative mixing of nodes in real-world networks gives important insights about the networks design and functionality, and has been analyzed in detail. However, this network-level measure conveys insufficient information about the local-level structure and motifs present in networks. We introduce a measure of local assortativeness that quantifies the level of assortative mixing for individual nodes in the context of the overall network. We show that such a measure, together with the resultant local assortativeness distributions for the network, is useful in analyzing network's robustness against targeted attacks. We also study local assortativeness in real-world networks, identifying different phases of network growth, showing that biological and social networks display markedly different local assortativeness distributions to technological networks, and discussing the implications to network design.