Edge Routing with Ordered Bundles

by Sergey Pupyrev, Lev Nachmanson, Sergey Bereg, and Alexander E. Holroyd

Abstract: Edge bundling reduces the visual clutter in a drawing of a graph by uniting the edges into bundles. We propose a method of edge bundling drawing each edge of a bundle separately as in metro-maps and call our method ordered bundles. To produce aesthetically looking edge routes it minimizes a cost function on the edges. The cost function depends on the ink, required to draw the edges, the edge lengths, widths and separations. The cost also penalizes for too many edges passing through narrow channels by using the constrained Delaunay triangulation. The method avoids unnecessary edge-node and edge-edge crossings. To draw edges with the minimal number of crossings and separately within the same bundle we develop an efficient algorithm solving a variant of the metro-line crossing minimization problem. In general, the method creates clear and smooth edge routes giving an overview of the global graph structure, while still drawing each edge separately and thus enabling local analysis.

Example: Tail graph

(a) Standard routing computed with the visibility graph approach. (b) Edge bundling routing


author = {Sergey Pupyrev and Lev Nachmanson and Sergey Bereg and Alexander E. Holroyd}, 
title = {Edge Routing with Ordered Bundles},
booktitle = {Proc. 19th Internat. Sympos. on Graph Drawing},
year = {2011}, 
series = {LNCS 7034},
pages = {136-147},
publisher = {Springer-Verlag},
year = {2011}