Further Towards Unambiguous Edge Bundling: Investigating Power-Confluent Drawings for Network Visualization

Abstract

Fig. 1. An illustration of our solution to the issues with the algorithm of Bach et al. [1], using their original example graph (Fig. 2 in [1]).From left to right: a conventional node-link diagram with vertices arranged around a circle; its power graph decomposition, where edges are compressed by grouping similar nodes together; our novel equivalent routing graph, where the nested structure of groups is represented by a directed tree; the resulting confluent drawing, where original edges are threaded through the routing graph to form bundled junctions.Abstract-Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and short-circuit problems, and solve both by modifying the routing graph to retain the hierarchical structure of power groups. We also classify the exact type of confluent drawings that the algorithm can produce as 'power-confluent', and prove that it is a subclass of the previously studied 'strict confluent' drawing. A description and source code of our implementation is also provided, which additionally includes an improved method for power graph construction.

Edge-Path Bundling: A Less Ambiguous Edge Bundling Approach

“…Their approach computes a power graph decomposition and uses the resulting hierarchy to both draw and bundle the network. Zheng et al [57] extend Bach et al [10] to create strict, power-confluent drawings, based on additional constraints that further reduce crossings and ambiguities.…”

“…For Confluent Drawings. we used an available implementation [5] based on the results of [10,57], which we modified to handle graphs with an embedding. This was realized by removing the layout step of the implementation and replacing it with the following.…”

“…Also, these approaches compute both the layout of the network and the bundling simultaneously. There have been a number of attempts to relax the strict constraints of confluent drawings to move towards unambiguous bundling [10,57], but all approaches still require the layout to be computed alongside the bundling.…”

Approximating the Bundled Crossing Number

“…Together with van Wijk, Holten introduced the idea of edge bundling to the area of information visualization [20,21]. Subsequently the concept was studied by many researchers, see for example [16,23,24,5,12,2,28,17]. In contrast to the concept of the bundled crossing number most algorithms used in information visualization for edge bundling are of heuristic nature and do not provide any guarantees on the quality of the solution.…”

“…These drawings were introduced by Dickerson et al [6] and subsequently studied by the graph drawing community [11,9,10,15,22]. Recently, these drawings were also picked up in more applied contexts, using heuristic approaches [2,28].…”