Metrics for dynamic networks

Many networks are dynamic in that their topology changes rapidly – on the same time-scale as the

communications of interest between network nodes. Examples are the human contact networks
involved in the transmission of disease, ad-hoc radio networks between moving vehicles, and the
transactions between principals in a market. While we have good models of static networks, so
far these have been lacking for the dynamic case. In this paper we present a simple but powerful
model, the time-ordered graph, which reduces a dynamic network to a static network with directed
flows. This enables us to extend network properties such as vertex degree, closeness and betweenness
centrality metrics in a very natural way to the dynamic case. We then demonstrate how our new
model applies to a number of interesting edge cases, such as where the network connectivity depends
on a small number of highly mobile vertices or edges, and show that our new centrality definition
allows us to graph the evolution of connectivity. Finally we apply our model and techniques to two
real-world dynamic graphs of human contact networks and then discuss the implication of temporal
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