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 different real-world networks and to detect their common patterns or differences. A systematic method that can characterize simultaneously the temporal and topological relations of the time-specific interactions (also called contacts or events) of a temporal network, is still missing. In this article, 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 the contacts from three perspectives: (1) the correlation (among the elements) of the activity time series which records the total number of contacts in a network that happen at each time step; (2) the interplay between the topological distance and time difference of two arbitrary contacts; (3) the temporal correlation of contacts within the local neighbourhood centred at each link (so-called ego-network) to explore whether such contacts that happen close in topology are also close in time. By applying our method to 13 real-world temporal networks, we found that temporal-Topological correlation of contacts is more evident in virtual contact networks than in physical contact networks. This could be due to the lower cost and easier access of online communications than physical interactions, allowing and possibly facilitating social contagion, that is, interactions of one individual may influence the activity of its neighbours. We also identify different patterns between virtual and physical networks and among physical contact networks at, for example, school and workplace, in the formation of correlation in local neighbourhoods. Patterns and differences detected via our method may further inspire the development of more realistic temporal network models, that could reproduce jointly temporal and topological properties of contacts.