Evaluating metrics in link streams.

Abstract

We seek to understand the topological and temporal nature of temporal networks by computing the distances, latencies and lengths of shortest fastest paths. Shortest fastest paths offer interesting insights about connectivity that were unknowable until recently. Moreover, distances and latencies tend to be computed by separate algorithms. We developed four algorithms that each compute all those values efficiently as a contribution to the literature. Two of those methods compute metrics from a fixed source temporal node. The other two, as a significant contribution to the literature, compute the metrics between all pairs of source and destination temporal nodes. The methods are also grouped by whether they work on paths with delays or not. Proofs of correctness for our algorithms are presented as well as bounds on their temporal complexities as functions of temporal network parameters. Experimental results show the algorithms presented perform well against the state of the art and terminate in decent time on real-world datasets. One purpose of this study is to help develop algorithms to compute centrality functions on temporal networks such as the betweenness centrality and the closeness centrality.