Unfolding Ordered Matrices into BioFabric Motifs

2026-02-23

AI Summary

Existing approaches struggle to automatically identify structural patterns in graphs and simultaneously optimize the ordering of both vertices and edges to produce high-quality BioFabric visualizations. This work proposes a novel method that jointly optimizes vertex and edge arrangements by leveraging an ordered adjacency matrix combined with Moran’s I spatial autocorrelation metric. Furthermore, it introduces a noise-robust pattern detection algorithm that, for the first time, enables the automatic “unfolding” of interpretable BioFabric motifs directly from the ordered matrix. The method effectively generates clear, pattern-enhanced visualizations on networks with up to 250 vertices, significantly improving users’ ability to grasp the global structure of complex networks at a glance.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Combinatorial Optimization
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Web data visualization
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• BioFabric
• graph layout
• vertex ordering
• edge ordering
• pattern recognition

Innovation

• BioFabric
• matrix ordering
• Moran's I
• motif detection
• graph visualization