Time-dependent personalized PageRank for temporal networks: Discrete and continuous scales

In this paper, we explore the PageRank of temporal networks (networks that evolve with time) with time-dependent personalization vectors. We consider both continuous and discrete time intervals and show that the PageRank of a continuous-temporal network can be nicely estimated by the PageRanks of the discrete-temporal networks arising after sampling. Additionally, precise boundaries are given for the estimated influence of the personalization vector on the ranking of a particular node. All ingredients in the classic PageRank definition, namely, the normalized matrix collecting the topology of the network, the damping factor, and the personalization vector are allowed, to the best of our knowledge, for the first time in the literature to vary independently with time. The theoretical results are illustrated by means of some real and synthetic examples.