Timestamped relational datasets consisting of records between pairs of entities are ubiquitous in data and network science. For applications like peer-to-peer communication, email, social network interactions, and computer network security, it makes sense to organize these records into groups based on how and when they are occurring. Weighted line graphs offer a natural way to model how records are related in such datasets but for large real-world graph topologies the complexity of building and utilizing the line graph is prohibitive. We present an algorithm to cluster the edges of a dynamic graph via the associated line graph without forming it explicitly. We outline a novel hierarchical dynamic graph edge clustering approach that efficiently breaks massive relational datasets into small sets of edges containing events at various timescales. This is in stark contrast to traditional graph clustering algorithms that prioritize highly connected community structures. Our approach relies on constructing a sufficient subgraph of a weighted line graph and applying a hierarchical agglomerative clustering. This work draws particular inspiration from HDBSCAN. We present a parallel algorithm and show that it is able to break billion-scale dynamic graphs into small sets that correlate in topology and time. The entire clustering process for a graph with $O(10 \text{ billion})$ edges takes just a few minutes of run time on 256 nodes of a distributed compute environment. We argue how the output of the edge clustering is useful for a multitude of data visualization and powerful machine learning tasks, both involving the original massive dynamic graph data and/or the non-relational metadata. Finally, we demonstrate its use on a real-world large-scale directed dynamic graph and describe how it can be extended to dynamic hypergraphs and graphs with unstructured data living on vertices and edges.