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Second-Order Assortative Mixing in Social Networks

Zhou, S; Cox, I; Hansen, LK; (2009) Second-Order Assortative Mixing in Social Networks.

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It is common to characterise networks based on their statistical properties. It has been shown that social networks, such as networks of co-starring film actors, collaborating scientists and email communicators, exhibit a positive first-order assortative behaviour, i.e. if two nodes are connected, then their degrees (the number of links a node has) are similar. For social networks, a node's degree has been assumed to be a proxy for its importance/prominence within the network, and the assortative behaviour is then interpreted as indicating that people mix with people of comparable prominence. In this paper we introduce a new property, second-order assortative mixing, which measures the correlation between the most prominent neighbours of two connected nodes, rather than the prominence of the nodes themselves. Five social networks and six other networks are examined. We observe very stronge second-order assortative mixing in social networks. This suggests that if two people interact in a social network then the importance of the most prominent person each knows is very likely to be the same. This is also true if we measure the average prominence of neighbours of the two people. This property is weaker or negative in non-social networks. We investigate a number of possible explanations for this property, including statistical significance, neighbourhood size, power-law degree distribution, cluster coefficient, triangles and bipartite graphs. However, none of these properties was found to provide an adequate explanation. We therefore conclude that second-order assortative mixing is a fundamental property of social networks.

Title:Second-Order Assortative Mixing in Social Networks
Keywords:physics.soc-ph, physics.soc-ph, physics.data-an
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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