Exploring the evolution of node neighborhoods in Dynamic Networks

Abstract

Dynamic Networks are a popular way of modeling and studying the behavior of evolving systems. However, their analysis constitutes a relatively recent subfield of Network Science, and the number of available tools is consequently much smaller than for static networks. In this work, we propose a method specifically designed to take advantage of the longitudinal nature of dynamic networks. It characterizes each individual node by studying the evolution of its direct neighborhood, based on the assumption that the way this neighborhood changes reflects the role and position of the node in the whole network. For this purpose, we define the concept of neighborhood event, which corresponds to the various transformations such groups of nodes can undergo, and describe an algorithm for detecting such events. We demonstrate the interest of our method on three real-world networks: DBLP, LastFM and Enron. We apply frequent pattern mining to extract meaningful information from temporal sequences of neighborhood events. This results in the identification of behavioral trends emerging in the whole network, as well as the individual characterization of specific nodes. We also perform a cluster analysis, which reveals that, in all three networks, one can distinguish two types of nodes exhibiting different behaviors: a very small group of active nodes, whose neighborhood undergo diverse and frequent events, and a very large group of stable nodes. density, network diameter (Leskovec et al. 2005a). Second, mesoscopic methods consider the network at an intermediary level, generally that of the community structure, e.g. modularity measure (Kashtan and Alon 2005), size of the communities (Backstrom et al. 2006). Finally, microscopic methods focus on individual nodes and possibly their direct neighborhood, e.g. clustering coefficient (Clauset and Eagle 2007).By definition, methods specifically designed to handle a dynamic network are more likely to take advantage of the specificity of such data. Regarding the granularity, if macroscopic and mesoscopic methods are widespread in the literature, it is not the case for microscopic methods. Yet, the benefits of such approaches are numerous: by allowing the tracking of finer evolution processes, they complement macroscopic and/or mesoscopic results. They help identifying behavioral trends among the network nodes, and consequently outliers. These results can facilitate the description and understanding of processes observed at a higher level, and can be useful to define models of the studied system, especially agent-based ones.In this work, we propose a method specifically designed to study dynamic slowly evolving networks, at the microscopic level. We characterize a node by the evolution of its neighborhood. More precisely, we detect specific events occurring among the groups of nodes constituting this neighborhood, between each pair of consecutive time slices, which we call neighborhood evolution events. This method constitutes our main contribution. To the best of our knowledge, it is the fir...

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