Description

Graph metrics, such as the simple but popular vertex degree and others based on it, are well-defined for static graphs. However, adapting static metrics for temporal graphs is still part of current research. In this paper, we propose a set of temporal extensions of four degree-dependent metrics, as well as aggregations like minimum, maximum, and average degree of (i) a vertex over a time interval and (ii) a graph at a specific point in time. We show why using the static degree can lead to wrong assumptions about the relevance of a vertex in a temporal graph and highlight the need to include time as a dimension in the metric. We propose a baseline algorithm to calculate the degree evolution of all vertices in a temporal graph and show its implementation in a distributed in-memory dataflow system. Using real-world and synthetic datasets containing up to 462 million vertices and 1.7 billion edges, we show the scalability of our algorithm on a distributed cluster achieving a speedup of around 12 on 16 machines.