The cluster faithfulness metrics CQ measure how faithfully the ground truth clustering of a graph is represented as the geometric clustering in a drawing of the graph. Existing CQ metrics use k-means clustering, which effectively compute a geometric clustering when the cluster sizes are even, resulting in accurate CQ metrics. However, k-means clustering tends to compute clusters of even sizes and thus often fails to compute an accurate geometric clustering when the cluster sizes are uneven, leading to inaccurate CQ metrics.In this paper, we present a new cluster faithfulness metric CQ-HAC, using HAC (Hierarchical Agglomerative Clustering). HAC can compute a more accurate geometric clustering for uneven cluster sizes than k-means clustering. Consequently, CQ-HAC can more accurately measure cluster faithfulness, regardless of whether the sizes of clusters are even or uneven. Moreover, we present two algorithms, Cluster-kmeans and Cluster-HAC, for optimizing cluster faithfulness of graph drawings. Extensive experiments show that in practice, both algorithms always compute perfectly cluster-faithful drawings (i.e., CQ = 1) in our experiments using various graphs with both even and uneven cluster sizes, achieving significant improvement over existing graph layouts, including cluster-focused layouts.

Recent works in graph visualization attempt to reduce the runtime ofrepulsionforce computation of force-directed algorithms using sampling. However, they fail to reduce the runtime forattractionforce computation to sublinear in the number of edges. We present theSubLinearForceframework for a fully sublinear-timeforce computationalgorithm for drawing large complex graphs. More precisely, we present new sublinear-time algorithms for theattraction forcecomputation of force-directed algorithms. We then integrate them with sublinear-time repulsion force computation to give a fully sublinear-time force computation. Extensive experiments show that our algorithms compute layouts on average 80% faster than the existing linear-time force computation algorithm, while obtaining significantly better quality metrics such as edge crossing and shape-based metrics.

Finding a shortest path for a given pair of vertices in a graph drawing is one of the fundamental tasks for qualitative evaluation of graph drawings. In this paper, we present the first machine learning approach to predict human shortest path task performance, including accuracy, response time, and mental effort. To predict the shortest path task performance, we utilize correlated quality metrics and the ground truth data from the shortest path experiments. Specifically, we introduce path faithfulness metrics and show strong correlations with the shortest path task performance. Moreover, to mitigate the problem of insufficient ground truth training data, we use the transfer learning method to pre-train our deep model, exploiting the correlated quality metrics. Experimental results using the ground truth human shortest path experiment data show that our models can successfully predict the shortest path task performance. In particular, model MSP achieves an MSE (i.e., test mean square error) of 0.7243 (i.e., data range from −17.27 to 1.81) for prediction.

Understanding what graph layout human prefer and why they prefer such graph layout is significant and challenging due to the highly complex visual perception and cognition system in human brain. In this paper, we present the first machine learning approach for predicting human preference for graph layouts.In general, the data sets with human preference labels are limited and insufficient for training deep networks. To address this, we train our deep learning model by employing the transfer learning method, e.g., exploiting the quality metrics, such as shape-based metrics, edge crossing and stress, which are shown to be correlated to human preference on graph layouts. Experimental results using the ground truth human preference data sets show that our model can successfully predict human preference for graph layouts. To our best knowledge, this is the first approach for predicting qualitative evaluation of graph layouts using human preference experiment data.

Recent works in graph visualization attempt to reduce the runtime of repulsion force computation of force-directed algorithms using sampling, however they fail to reduce the runtime for attraction force computation to sublinear in the number of edges.We present new sublinear-time algorithms for the attraction force computation of force-directed algorithms and integrate them with sublinear-time repulsion force computation.Extensive experiments show that our algorithms, operated as part of a fully sublinear-time force computation framework, compute graph layouts on average 80% faster than existing linear-time force computation algorithm, with surprisingly significantly better quality metrics on edge crossing and shape-based metrics.

Abstract In this paper, we present a new framework for sublinear time force computation for visualization of big complex graphs. Our algorithm is based on the sampling of vertices for computing repulsion forces and edge sparsification for attraction force computation. More specifically, for vertex sampling, we present three types of sampling algorithms, including random sampling, geometric sampling, and combinatorial sampling, to reduce the repulsion force computation to sublinear in the number of vertices. We utilize a spectral sparsification approach to reduce the number of attraction force computations to sublinear in the number of edges for dense graphs. We also present a smart initialization method based on radial tree drawing of the BFS spanning tree rooted at the center. Experiments show that our new sublinear time force computation algorithms run quite fast, while producing good visualization of large and complex networks, with significant improvements in quality metrics such as shape‐based and edge crossing metrics.