Unfolding Ordered Matrices into BioFabric Motifs

TL;DR

This paper presents a new method for automatically ordering vertices and edges in BioFabric visualizations by using well-ordered matrices and pattern detection, improving clarity for large graphs.

Contribution

It introduces an efficient pipeline that uses Moran's I and pattern detection to produce high-quality BioFabric layouts for graphs with up to 250 vertices.

Findings

Successfully orders graphs with up to 250 vertices

Detects patterns in adjacency matrices using Moran's I

Unfolds matrices into clear BioFabric visualizations

Abstract

BioFabrics were introduced by Longabaugh in 2012 as a way to draw large graphs in a clear and uncluttered manner. The visual quality of BioFabrics crucially depends on the order of vertices and edges, which can be chosen independently. Effective orders can expose salient patterns, which in turn can be summarized by motifs, allowing users to take in complex networks at-a-glance. However, so far there is no efficient layout algorithm which automatically recognizes patterns and delivers both a vertex and an edge ordering that allows these patterns to be expressed as motifs. In this paper we show how to use well-ordered matrices as a tool to efficiently find good vertex and edge orders for BioFabrics. Specifically, we order the adjacency matrix of the input graph using Moran's $I$ and detect (noisy) patterns with our recent algorithm. In this note we show how to "unfold" the ordered matrix and its patterns into a high-quality BioFabric. Our pipelines easily handles graphs with up to 250 vertices.