  How do vertices exert influence in graph data? We develop a framework for
edge clustering, a new method for exploratory data analysis that reveals how
both vertices and edges collaboratively accomplish directed influence in
graphs, especially for directed graphs. In contrast to the ubiquitous vertex
clustering which groups vertices, edge clustering groups edges. Edges sharing a
functional affinity are assigned to the same group and form an influence
subgraph cluster. With a complexity comparable to that of vertex clustering,
this framework presents three different methods for edge spectral clustering
that reveal important influence subgraphs in graph data, with each method
providing different insight into directed influence processes. We present
several diverse examples demonstrating the potential for widespread application
of edge clustering in scientific research.
