Lifetime-preserving reference models for characterizing spreading dynamics on temporal networks

Abstract

To study how a certain network feature affects processes occurring on a temporal network, one often compares properties of the original network against those of a randomized reference model that lacks the feature in question. The randomly permuted times (PT) reference model is widely used to probe how temporal features affect spreading dynamics on temporal networks. However, PT implicitly assumes that edges and nodes are continuously active during the network sampling period - an assumption that does not always hold in real networks. We systematically analyze a recently-proposed restriction of PT that preserves node lifetimes (PTN), and a similar restriction (PTE) that also preserves edge lifetimes. We use PT, PTN, and PTE to characterize spreading dynamics on (i) synthetic networks with heterogeneous edge lifespans and tunable burstiness, and (ii) four real-world networks, including two in which nodes enter and leave the network dynamically. We find that predictions of spreading speed can change considerably with the choice of reference model. Moreover, the degree of disparity in the predictions reflects the extent of node/edge turnover, highlighting the importance of using lifetime-preserving reference models when nodes or edges are not continuously present in the network.