Identifying important nodes in networks is essential to analysing their structure and understanding their dynamical processes. In addition, myriad real systems are time-varying and can be represented as temporal networks. Motivated by classic gravity in physics, we propose a temporal gravity model to identify important nodes in temporal networks. In gravity, the attraction between two objects depends on their masses and distance. For the temporal network, we treat basic node properties (e.g., static and temporal properties) as the mass and temporal characteristics (i.e., fastest arrival distance and temporal shortest distance) as the distance. Experimental results on 10 real datasets show that the temporal gravity model outperforms baseline methods in quantifying the structural influence of nodes. When using the temporal shortest distance as the distance between two nodes, the proposed model is more robust and more accurately determines the node spreading influence than baseline methods. Furthermore, when using the temporal information to quantify the mass of each node, we found that a novel robust metric can be used to accurately determine the node influence regarding both network structure and information spreading.

Many systems are dynamic and time-varying in the real world. Discovering the vital nodes in temporal networks is more challenging than that in static networks. In this study, we proposed a temporal information gathering (TIG) process for temporal networks. The TIG-process, as a node's importance metric, can be used to do the node ranking. As a framework, the TIG-process can be applied to explore the impact of temporal information on the significance of the nodes. The key point of the TIG-process is that nodes' importance relies on the importance of its neighborhood. There are four variables: temporal information gathering depth n, temporal distance matrix D, initial information c, and weighting function f. We observed that the TIG-process can degenerate to classic metrics by a proper combination of these four variables. Furthermore, the fastest arrival distance based TIG-process (fad-tig) is performed optimally in quantifying nodes' efficiency and nodes' spreading influence. Moreover, for the fad-tig process, we can find an optimal gathering depth n that makes the TIG-process perform optimally when n is small.