Topological-temporal properties of evolving networks

Many real-world complex systems including human interactions can be represented by temporal (or evolving) networks, where links activate or deactivate over time. Characterizing temporal networks is crucial to compare such systems and to study the dynamical processes unfolding on them. A systematic method to characterize simultaneously the temporal and topological relations of active links (also called contacts or events), in order to compare different real-world networks and to detect their common patterns or differences is still missing. In this paper, we propose a method to characterize to what extent contacts that happen close in time occur also close in topology. Specifically, we study the interrelation between temporal and topological properties of contacts from three perspectives: (1) the autocorrelation of the time series recording the total number of contacts happened at each time step in a network; (2) the interplay between the topological distance and interevent time of two contacts; (3) the temporal correlation of contacts within local neighborhoods beyond a node pair. By applying our method on 13 real-world temporal networks, we found that temporal-topological correlation of contacts is more evident in virtual contact networks than in physical contact ones. This could be due to the lower cost and easier access of online communications than physical interactions, allowing and possibly facilitating social contagion, i.e., interactions of one individual may influence the activity of its neighbors. We also identify different patterns between virtual and physical networks and among physical contact networks at, e.g., school and workplace, in the formation of correlation in local neighborhoods. Detected patterns and differences may further inspire the development of more realistic temporal network models, that could reproduce jointly temporal and topological properties of contacts.