Six methods for transforming layered hypergraphs to apply layered graph layout algorithms

Abstract

Hypergraphs are a generalization of graphs in which edges (hyperedges) can connect more than two vertices—as opposed to ordinary graphs where edges involve only two vertices. Hypergraphs are a fairly common data structure but there is little consensus on how to visualize them. To optimize a hypergraph drawing for readability, we need a layout algorithm. Common graph layout algorithms only consider ordinary graphs and do not take hyperedges into account. We focus on layered hypergraphs, a particular class of hypergraphs that, like layered graphs, assigns every vertex to a layer, and the vertices in a layer are drawn aligned on a linear axis with the axes arranged in parallel. In this paper, we propose a general method to apply layered graph layout algorithms to layered hypergraphs. We introduce six different transformations for layered hypergraphs. The choice of transformation affects the subsequent graph layout algorithm in terms of computational performance and readability of the results. Thus, we perform a comparative evaluation of these transformations in terms of number of crossings, edge length, and impact on performance. We also provide two case studies showing how our transformations can be applied to real‐life use cases. A copy of this paper with all appendices and supplemental material is available at osf.io/grvwu.

Exploring the Design Space of BioFabric Visualization for Multivariate Network Analysis

“…Reordering Among the elements that most definitely will influence the perception of network topology in BioFabric, there is the ordering of the nodes and edges. The problem has been mentioned — although without proposed solutions — already in previous research [VBP*21, DBPB*22]. Indeed, the superficial and inattentive combination of the order of the two sets of network elements can produce unnecessarily longer, harder‐to‐track edges — while, conversely, using clever sorting strategies might create structures in the visualization that can help highlight topological features, such as the staircase pattern shown in Figure 6.…”

“…It should be taken into account that the effectiveness of BioFabric is also affected by node and edge ordering [VBP*21,DBPB*22] — an aspect that is not considered in the scope of this paper. Instead, we focus on the encoding of additional data dimensions into the visualization, which can be applied to any ordering of nodes and edges.…”

Layered graphs and their layouts, evaluations, and applications

“…Six methods for transforming layered hypergraphs to apply layered graph layout algorithms [81] EuroVis 2022 osf.io/grvwu…”

“…To illustrate how a researcher can use this paper, we will describe how we designed one of our computational evaluations. Di Bartolomeo et al [81] were tasked with representing a network of authors collaborating on VIS papers. Thus, the starting point was the D dataset.…”

“…In terms of choice of what M metrics to report, layered graphs aren't particularly noteworthy and often report the most common metrics such as running time and the number of crossings, sometimes including edge length Chapter 6 -Evaluating graph layout algorithms [81,286,83,164,170,86] or edge bends [304,202,86]. Area and aspect ratio aren't particularly concerning when drawing layered graphs due to the already constraining nature of layers.…”