Persistence and periodicity in a dynamic proximity network

Abstract: The topology of social networks can be understood as being inherently dynamic, with edges having a distinct position in time. Most characterizations of dynamic networks discretize time by converting temporal information into a sequence of network "snapshots" for further analysis. Here we study a highly resolved data set of a dynamic proximity network of 66 individuals. We show that the topology of this network evolves over a very broad distribution of time scales, that its behavior is characterized by strong periodicities driven by external calendar cycles, and that the conversion of inherently continuous-time data into a sequence of snapshots can produce highly biased estimates of network structure. We suggest that dynamic social networks exhibit a natural time scale \Delta_{nat}, and that the best conversion of such dynamic data to a discrete sequence of networks is done at this natural rate.