MoN8: Eighth Mathematics of Networks meeting – 18th September 2009, Cambridge University

Shi Zhou (UCL) – Second-order mixing in network

An analysis of several large social networks suggests that there is truth to the adage “it’s who you know.” Previous work showed that nodes in a social network prefer to mix with nodes of similar importance, it being assumed that the number of links to a node is a measure of the node’s prominence. However, we report a very much stronger relationship. If two nodes are connected and we look at each node’s most prominent neighbour, very likely these two neighbours have almost identical importance. In fact, much of the time, they are one and the same node. Moreover, this property holds across a wide range of prominence values, and across a wide variety of social networks. The property is weaker or absent in other types of networks such as the Internet and protein interactions. Our work reveals a new dimension to the hierarchical structure present in social networks, i.e. comparing with the number of people we know, collaboration is much more strongly determined by our single most important contact.

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Contact: Richard G. Clegg ( or Keith Briggs (mailto:keith.briggs_at_bt_dot_com)