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：BioFabric由Longabaugh于2012年提出，作为一种以清晰简洁方式绘制大型图的方法。BioFabric的视觉质量关键取决于顶点和边的排序，二者可独立选择。有效的排序能突显显著模式，这些模式进而可通过基元进行概括，使用户能够一目了然地理解复杂网络。然而，目前尚无高效的布局算法能够自动识别模式，并提供同时允许这些模式以基元形式表达的顶点与边排序。本文展示了如何利用有序矩阵作为工具，为BioFabric高效寻找优质的顶点与边排序。具体而言，我们使用Moran's $I$对输入图的邻接矩阵进行排序，并利用我们近期提出的算法检测（含噪声的）模式。本说明阐述了如何将有序矩阵及其模式“展开”为高质量的BioFabric。我们的流程可轻松处理包含多达250个顶点的图。