Inferring waiting time distributions of temporal networks using unicast-based active sampling

Recent empirical evidence from research on temporal networks has shown that the time constraints imposed on individual interactions are crucial for understanding the generic structure and dynamics of networks. A desirable but challenging task is sampling the waiting time distribution (WTD) associated with their internal interactions, a defining feature that reflects the added time dimension of temporal networks. Here, the random-walk exploration techniques for static networks are extended to adapt to this time-extended inferential problem. Specifically, an active unicast protocol is proposed where random walk is assumed to occur at the moment of the α-th appearance of outgoing temporal link, with parameter α unnecessarily equal to 1. Using the ”Redistribute-to-the-Right” imputation technique, it is found that this purposely delayed transition mechanism of random walk allows correct reCovery of the entire distributional shape of underlying WTDs, including a variety of empirically relevant, non-Poissonian cases. Numerical results also verify the validity of the proposed self-consistent iterative estimator for WTDs. The proposed scheme provides an effective and flexible route for active sampling of temporal networks and can be extended in a broad array of applications.