Identifying important nodes based on upstream and downstream time-respecting paths in temporal networks

Identifying the nodes that play significant roles in the epidemic spreading process has attracted extensive attention in recent years. Few centrality measures, such as temporal degree and temporal closeness centrality, have been proposed to quantify node importance based on the topological structure of social contact networks. Most methods estimate the importance of a node from a single aspect, e.g. a higher degree in time snapshot graphs, or shorter distances to other nodes along time-respecting paths. However, this may not be the case in the real world. On the one hand, a node with more nodes on its out streams (i.e. downstream) should be more important because it may affect more nodes along its time-stamped contacting paths once it is infected. On the other hand, a node with more nodes in its in streams (i.e. upstream) deserves closer attention, as it has a higher probability of infection by other nodes. We propose a new temporal centrality measure, upstream and downstream centrality (UD-centrality) with two forms of realizations, i.e. a linear UD-centrality (L-UD) and a product UD-centrality (P-UD) to estimate the importance of nodes based on the temporal structures of social contact networks. We compare our L-UD and P-UD to three classic temporal network centralities through simulations on 14 real-world temporal networks based on the susceptible-infected (SI) model. The comparison results show that UD-centrality can more accurately rank the importance of nodes than the baseline centrality measures.