Network Reachability Analysis on Temporally Varying Interaction Networks

Abstract

Tremendous effort has been made in understanding the network connectivity and reachability in the spacial domain in the past decades. However, few of them focuses on time-varying the network connectivity and reachability problem in the time domain, which nevertheless exists in the most popular interactive networks, e.g., interactive forums, websites, tweeter-like online social applications, and etc. In this paper, we formulate the reachability problem in such interactive networks, and provide a novel way of quantitatively analyzing the reachability problem via the reverse chronological order. Based on real data, we further demonstrate the analytical power of our theoretical design and show that such reachability problem can be further modeled in a random digraph and a Markov process where time intervals obey exponential distribution $\mathbb {D}$ with the appearance of interaction edges following a Poisson process. In the extensive experiment study, we collect all the interaction behaviors such as reply and forward in recent 10 years from the largest forums in China (specifically, Tianya) with more than 3 million of daily active users. The experiment results show that there is a good match between the theoretical results and the real data.