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 ∆nat, and that the best conversion of such dynamic data to a discrete sequence of networks is done at this natural rate. Complex systems of interacting components are now often represented as a network, i.e., n nodes or vertices joined together in pairs by m links or edges. Characterizing these networks' topological patterns can often yield significant insights into the structure and function of the original system [1-3], and networks from a wide variety of domains, including social [4-6], technological [7] [8] [9] and biological [10] [11] [12] systems, have been studied in this way. From this kind of network analysis, it has been demonstrated that many real-world networks exhibit similar properties. For instance, most real-world networks exhibit a highly heterogeneous degree distribution and short topological distances between arbitrary vertices. Social networks differ from many other kinds of networks [13] , for instance, by having a larger-than-expected density of short loops (typically triangles -the so-called "clustering coefficient" although the behavior seems to generalize to short loops of all lengths). Further, social networks exhibit a pattern in connectivity at the wholenetwork level that is often called "community structure," in which large and relatively dense subgraphs are themselves sparsely connected together [14] , as well as assortative mixing on various node attributes [15] . Much of our understanding of the large-scale structural patterns in social networks has come from the study of static topologies -an idealization that naturally omits any dynamic or time-evolving character of the social processes that underly these networks. For some scientific questions, a static topology may be sufficient. However, for questions regarding dynamics, the temporal variation of edges themselves is likely to be important. For instance, in the spread of an epidemic, the order of inter- * Published in the proceedings of the DIMACS Workshop on Computational Methods for Dynamic Interaction Networks (Piscataway), 2007. action can have a significant effect on which individuals become infected, and ultimately the size of an epidemic outbreak, e.g., if two individuals A and B interact prior to A being infected, but not after, then B has no risk of infection, a dynamic that is difficult to capture with static topologies (Fig. 1) . Unfortunately, temporal connectivity data is often difficult to obtain for real social systems. The traditional approach to studying network dynamics in sociology (see, for instance, [16] and reference therein) tends to rely heavily on interaction data self-reported by study participants, which exhibit significant bias and noise [17] . Several recent studies in physics and computer science have utilized web-based or other indirect sources of dynamic social network data [18] [19] [20] [21] [22] [23] . In general, empirical studies convert the available temporal data into a short sequence of non-overlapping network "snapshots," (called "panel data" in the sociology literature [24] ), each of a length of time greater than the natural time scale of topological variation. This sequence can then be further
In REF , a dynamic proximity network is modeled and analyzed to find the properties of human interaction dynamics.
Persistence and periodicity in a dynamic proximity network
ArXiv
ArXiv
Mathematics Physics Computer Science