Static Representation Of Temporal Network Based On Spreading Dynamics

Temporal network is included with the additional degree of freedom of time, which is different from static network. This has brought new challenges to theoretical analysis and numerical simulations. Most existing investigations about the topological structure of network are based on the assumption that the underlying network is static whose topological structure keeps unchanged with time evolution. The static network without considering the time sequence of events, however, cannot precisely reproduce the topological properties of some complex systems. To facilitate the study of complex systems, we hope to propose an appropriate method to represent temporal network as static network.In the present paper, a new method is proposed based on time-slice network. To represent the temporal network as the static one, the key point is to find an optimal time-window At. We apply new method to two different empirical data sets, and analyze the degree and betweenness centrality of the nodes of generated static network. We find that the average degree over nodes increases with the size of time-window, while the average betweenness centrality increases with Δt firstly, and then almost keeps unchanged. The correlations between the degree and the betweenness centrality of time-window are also analyzed. Results show that topology measures of static networks are located in a wide range with the increasing of At accompanied with some fluctuations.This paper aims at studying static representations of temporal networks by combining with spreading dynamics process, which provides a new insight into understanding the topological structure of temporal network. We focus at whether topological properties of a single node in the static representation could measure its importance in the process of disease spreading. We simulate disease spread using Susceptible-Infected-Recovered (SIR) model. The size of disease outbreak Ω of each individual node is investigated by considering the infected probability λ and the ratio between the duration of disease spreading and time range T δ. The spearman’s rank correlation coefficient, denoted by p, is introduced to quantify the correlation between the topological property of static representation and disease outbreak size in temporal network. Larger p indicates a better representation. Simulation results display that, the correlation coefficient p between network’s topological structure and the size of disease outbreak is much larger, if the time for disease spreading δ is long enough and disease transmission probability λ is smaller.