Biclique edge cover graphs and confluent drawings

Abstract

Confluent drawing is a technique that allows some non-planar graphs to be visualized in a planar way. This approach merges edges together, drawing groups of them as single tracks, similar to train tracks. In the general case, producing confluent drawings automatically has proven quite difficult. We introduce the biclique edge cover graph that represents a graph G as an interconnected set of cliques and bicliques. We do this in such a way as to permit a straightforward transformation to a confluent drawing of G. Our result is a new sufficient condition for confluent planarity and an additional algorithmic approach for generating confluent drawings. We give some experimental results gauging the performance of existing confluent drawing heuristics. © Springer-Verlag Berlin Heidelberg 2007.