Ranking the key nodes with temporal degree deviation centrality on complex networks

Records of time-stamped social interactions between pairs of individuals (e.g. the human contact networks involved in the transmission of disease, ad hoc radio networks between moving vehicles, and the transactions between principals in a market) constitute a so-called temporal network. A remarkable difference between temporal networks and conventional static networks is that time-stamped events rather than links are the unit elements generating the collective behavior of nodes. While we have good centralities to measure the importance of the nodes in static networks, so far these have been lacking for temporal cases. In this paper we propose a simple but powerful centrality, the degree deviation centrality, which calculates the deviation of temporal degree centrality. This enables us to extend network properties vertex degree centrality metrics in a very natural way to the temporal case. We then demonstrate how our centrality applies to identify the vital nodes in temporal networks by epidemic spreading dynamics based on SI (susceptible-infected) model. The numerical experiments on several real networks indicate that the temporal degree deviation centrality method outperforms some other indicators, and the results with different time window size show that the improvement is also robust.