Metrics for dynamic networks

There’s a huge literature on the properties of static or slowly-changing social networks, such as the pattern of friends on Facebook, but almost nothing on networks that change rapidly. But many networks of real interest are highly dynamic. Think of the patterns of human contact that can spread infectious disease; you might be breathed on by a hundred people a day in meetings, on public transport and even in the street. Yet if we were facing a flu pandemic, how could we measure whether the greatest spreading risk came from high-order static nodes, or from dynamic ones? Should we close the schools, or the Tube?

Today we unveiled a paper which proposes new metrics for centrality in dynamic networks. We wondered how we might measure networks where mobility is of the essence, such as the spread of plague in a medieval society where most people stay in their villages and infection is carried between them by a small number of merchants. We found we can model the effects of mobility on interaction by embedding a dynamic network in a larger time-ordered graph to which we can apply standard graph theory tools. This leads to dynamic definitions of centrality that extend the static definitions in a natural way and yet give us a much better handle on things than aggregate statistics can. I spoke about this work today at a local workshop on social networking, and the paper’s been accepted for Physical Review E. It’s joint work with Hyoungshick Kim.

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