Mining large-scale trajectory data streams (of moving objects) has attracted significant attention due to an abundance of modern tracking devices and a number of real-world applications. In this paper, we are interested in evaluating the relative importance of such objects through monitoring their interactions with other objects, over time. Which object has encountered more other objects? When did these encounters happen and how long did they last? To address this type of questions, we consider a trajectory network that is defined based on the proximity of moving objects over time. Given this network, we are able to evaluate the importance of an object (node) by monitoring its complex network connections to other nodes over time. Traditional approaches to address the problem rely on either evaluating network metrics over a number of static network snapshots or expensive trajectory similarity and clustering methods that require further post-processing. Streaming algorithms also exist, but they focus on simple network metrics. In contrast to these approaches, we devise a method that is able to simultaneously evaluate node importance metrics for all moving objects in the trajectory network. Our proposed method is based on, first, efficiently computing and representing the interactions of moving objects as time intervals. Then, a fast and accurate one-pass sweep-line algorithm over the trajectories (SLOT) is devised that can effectively compute the metrics of interest, all at once. Through experiments on various types of data, we demonstrate that our algorithm is a multitude of times faster than sensible baselines, for a varying range of conditions.