Undirected graphs are frequently used to model networks. The topology of an undirected graph G can be captured by an adjacency matrix; this matrix in turn can be visualized directly to give insight into the graph structure. Which visual patterns appear in such a matrix visualization depends on the ordering of its rows and columns. Formally defining the quality of an ordering and then automatically computing a high-quality ordering are both challenging problems; however, effective heuristics exist and are used in practice. Often, graphs exist as part of a collection of graphs on the same set of vertices. To visualize such graph collections, we need a single ordering that works well for all matrices simultaneously. The current state-of-the-art solves this problem by taking a (weighted) union over all graphs and applying existing heuristics. However, this union leads to a loss of information, specifically in those parts of the graphs which are different. We propose a collection-aware approach to avoid this loss of information and apply it to two popular heuristic methods: leaf order and barycenter. The de-facto standard computational quality metrics for matrix ordering capture only block-diagonal patterns (cliques). Instead, we propose to use Moran's I, a spatial auto-correlation metric, which captures the full range of established patterns. The popular leaf order method heuristically optimizes a similar measure which supports the use of Moran's I in this context. We evaluated our methods for simultaneous orderings on real-world datasets using Moran's I as the quality metric. Our results show that our collection-aware approach matches or improves performance compared to the union approach, depending on the similarity of the graphs in the collection. Specifically, our Moran's I-based collection-aware leaf order implementation consistently outperforms other implementations.
翻译:非定向图形经常被用于模拟网络。 一个未定向图形 G 的表层可以被匹配矩阵捕获; 这个矩阵可以被直接视觉化, 以洞察图形结构。 在这样的矩阵中显示的视觉模式取决于其行和列的顺序。 正式定义订单的质量, 然后自动计算高质量的订单, 这些都是具有挑战性的问题; 但是, 有效的顺差存在, 并在实践中使用 。 通常, 图表可以作为同一套顶端上的图集的一部分。 要视觉化这样的图表收藏, 我们需要一个对所有矩阵同时运作良好的单一命令。 目前这种矩阵中的视觉模式取决于其行和列的顺序的顺序。 但是, 这个组合会导致信息丢失, 特别是在图表中不同的部分。 我们提议一种收集认知的方法, 以避免信息损失, 并将其应用到两种流行性高压方法: 叶序和巴里基罗雅的收藏, 将我们的标准货币模式的模型化质量 用于持续地计算, 将我们的标准货币序列的运行方式用于我们的数据采集系统。