Edge Compression Techniques for Visualization of Dense Directed Graphs

Abstract

We explore the effectiveness of visualizing dense directed graphs by replacing individual edges with edges connected to 'modules'-or groups of nodes-such that the new edges imply aggregate connectivity. We only consider techniques that offer a lossless compression: that is, where the entire graph can still be read from the compressed version. The techniques considered are: a simple grouping of nodes with identical neighbor sets; Modular Decomposition which permits internal structure in modules and allows them to be nested; and Power Graph Analysis which further allows edges to cross module boundaries. These techniques all have the same goal--to compress the set of edges that need to be rendered to fully convey connectivity--but each successive relaxation of the module definition permits fewer edges to be drawn in the rendered graph. Each successive technique also, we hypothesize, requires a higher degree of mental effort to interpret. We test this hypothetical trade-off with two studies involving human participants. For Power Graph Analysis we propose a novel optimal technique based on constraint programming. This enables us to explore the parameter space for the technique more precisely than could be achieved with a heuristic. Although applicable to many domains, we are motivated by--and discuss in particular--the application to software dependency analysis.

HOLA: Human-like Orthogonal Network Layout

“…The second possible improvement is extending HOLA to better handle dense graphs through integration of automatic cloning [15], edge-bundling [17] and compression techniques [10].…”

High-Quality Ultra-Compact Grid Layout of Grouped Networks

“…Density (|edges|/|nodes|) ranges from tree-like (∼ 1) to quite dense (1.61). We generated the flat scale-free graphs based on the model proposed by Bollobás et al [17], with 10 graphs for each graph size from 7 to 100 nodes. In these generated graphs we controlled for edge density such that |edges|/|nodes| is up to 1.22.…”

“…Part of the motivation for this work was the search for an effective layout method for edge-compressed dense, directed networks [17]. Without compression, graphs that have only few nodes but many edges are already very difficult to read.…”

“…This containment then enables the use of the power-graph convention [45] to collapse edges. In such an edgecompressed view [17] an edge from a group to another group implies all nodes in the first group are connected to all nodes in the second. Unlike virtually all existing approaches to power-graphs or network diagrams with clustering, we do not require that groups are hierarchical, making our approach applicable to other types of diagrams such as representations of overlapping set-membership (Fig.…”

Untangling the Hairballs of Multi-Centered, Small-World Online Social Media Networks

“…Various approaches to reduce the clutter in drawings of small worlds and other hairball graphs have been proposed [21], most notably edge bundling [17,30], edge lensing [20], modified layout algorithms [3] or representations [1,11,27,43], and graph simplification [2,29,32,34,37,42,44]. The idea of graph simplification is to identify a subset of edges such that only the resulting graph, the so-called backbone, needs to be laid out.…”