Linear layouts are a graph visualization method that can be used to capture an entry pattern in an adjacency matrix of a given graph. By reordering the node indices of the original adjacency matrix, linear layouts provide knowledge of latent graph structures. Conventional linear layout methods commonly aim to find an optimal reordering solution based on predefined features of a given matrix and loss function. However, prior knowledge of the appropriate features to use or structural patterns in a given adjacency matrix is not always available. In such a case, performing the reordering based on data-driven feature extraction without assuming a specific structure in an adjacency matrix is preferable. Recently, a neural-network-based matrix reordering method called DeepTMR has been proposed to perform this function. However, it is limited to a two-mode reordering (i.e., the rows and columns are reordered separately) and it cannot be applied in the one-mode setting (i.e., the same node order is used for reordering both rows and columns), owing to the characteristics of its model architecture. In this study, we extend DeepTMR and propose a new one-mode linear layout method referred to as AutoLL. We developed two types of neural network models, AutoLL-D and AutoLL-U, for reordering directed and undirected networks, respectively. To perform one-mode reordering, these AutoLL models have specific encoder architectures, which extract node features from an observed adjacency matrix. We conducted both qualitative and quantitative evaluations of the proposed approach, and the experimental results demonstrate its effectiveness.

翻译：线性布局是一种图可视化方法，可用于捕捉给定图邻接矩阵中的条目模式。通过重新排序原始邻接矩阵的节点索引，线性布局能够揭示潜在的图结构信息。传统的线性布局方法通常基于预定义的矩阵特征与损失函数来寻找最优重排序方案。然而，在实际应用中，往往难以预先确定应使用的特征或邻接矩阵中存在的结构模式。在此情况下，基于数据驱动的特征提取进行重排序（无需假设邻接矩阵具有特定结构）是更可取的方案。近期提出的基于神经网络的矩阵重排序方法DeepTMR实现了这一功能，但由于其模型架构特性，该方法仅限于双模重排序（即行与列分别独立重排序），无法应用于单模场景（即使用相同节点顺序同时对行与列进行重排序）。本研究扩展了DeepTMR方法，提出了一种称为AutoLL的新型单模线性布局方法。我们开发了两种神经网络模型：分别针对有向网络和无向网络重排序的AutoLL-D与AutoLL-U。为实现单模重排序，这些AutoLL模型采用特定的编码器架构，从观测到的邻接矩阵中提取节点特征。我们通过定性与定量评估对所提方法进行了验证，实验结果表明了该方法的有效性。