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.

翻译：生物织物由Longabaugh于2012年提出，作为一种以清晰无杂乱方式绘制大型图的方法。生物织物的视觉质量关键取决于顶点和边的顺序，这两者可以独立选择。有效的顺序能够暴露显著的模式，这些模式进而可通过结构基元进行概括，使用户能够一目了然地把握复杂网络。然而，目前尚缺乏一种能够自动识别模式并提供顶点和边排序的高效布局算法，使得这些模式得以表达为结构基元。本文展示了如何利用有序矩阵作为工具，高效地为生物织物寻找优质的顶点和边顺序。具体而言，我们使用Moran's $I$对输入图的邻接矩阵进行排序，并借助我们近期提出的算法检测（含噪声的）模式。在本报告中，我们展示了如何将有序矩阵及其模式"展开"为高质量的生物织物。我们的处理流程能轻松应对顶点数高达250的图。