Computing top-k temporal closeness in temporal networks

The closeness centrality of a vertex in a classical static graph is the reciprocal of the sum of the distances to all other vertices. However, networks are often dynamic and change over time. Temporal distances take these dynamics into account. In this work, we consider the harmonic temporal closeness with respect to the shortest duration distance. We introduce an efficient algorithm for computing the exact top-k temporal closeness values and the corresponding vertices. The algorithm can be generalized to the task of computing all closeness values. Furthermore, we derive heuristic modifications that perform well on real-world data sets and drastically reduce the running times. For the case that edge traversal takes an equal amount of time for all edges, we lift two approximation algorithms to the temporal domain. The algorithms approximate the transitive closure of a temporal graph (which is an essential ingredient for the top-k algorithm) and the temporal closeness for all vertices, respectively, with high probability. We experimentally evaluate all our new approaches on real-world data sets and show that they lead to drastically reduced running times while keeping high quality in many cases. Moreover, we demonstrate that the top-k temporal and static closeness vertex sets differ quite largely in the considered temporal networks.

The phantom steering effect in Q&A websites

Virtual rewards, such as badges, are commonly used in online platforms as incentives for promoting contributions from a userbase. It is widely accepted that such rewards “steer” people’s behaviour towards increasing their rate of contributions before obtaining the reward. This paper provides a new probabilistic model of user behaviour in the presence of threshold rewards, such a badges. We find, surprisingly, that while steering does affect a minority of the population, the majority of users do not change their behaviour around the achievement of these virtual rewards. In particular, we find that only approximately 5–30% of Stack Overflow users who achieve the rewards appear to respond to the incentives. This result is based on the analysis of thousands of users’ activity patterns before and after they achieve the reward. Our conclusion is that the phenomenon of steering is less common than has previously been claimed. We identify a statistical phenomenon, termed “Phantom Steering”, that can account for the interaction data of the users who do not respond to the reward. The presence of phantom steering may have contributed to some previous conclusions about the ubiquity of steering. We conduct a qualitative survey of the users on Stack Overflow which supports our results, suggesting that the motivating factors behind user behaviour are complex, and that some of the online incentives used in Stack Overflow may not be solely responsible for changes in users’ contribution rates.