DRGraph: An Efficient Graph Layout Algorithm for Large-scale Graphs by Dimensionality Reduction

Force-Directed Graph Layouts Revisited: A New Force Based on the T-Distribution

In this article, we propose the t-FDP model, a force-directed placement method based on a novel bounded short-range force (t-force) defined by Student's t-distribution. Our formulation is flexible, exerts limited repulsive forces for nearby nodes and can be adapted separately in its short- and long-range effects. Using such forces in force-directed graph layouts yields better neighborhood preservation than current methods, while maintaining low stress errors. Our efficient implementation using a Fast Fourier Transform is one order of magnitude faster than state-of-the-art methods and two orders faster on the GPU, enabling us to perform parameter tuning by globally and locally adjusting the t-force in real-time for complex graphs. We demonstrate the quality of our approach by numerical evaluation against state-of-the-art approaches and extensions for interactive exploration.

Graph Exploration With Embedding-Guided Layouts

Node-link diagrams are widely used to visualize graphs. Most graph layout algorithms only use graph topology for aesthetic goals (e.g., minimize node occlusions and edge crossings) or use node attributes for exploration goals (e.g., preserve visible communities). Existing hybrid methods that bind the two perspectives still suffer from various generation restrictions (e.g., limited input types and required manual adjustments and prior knowledge of graphs) and the imbalance between aesthetic and exploration goals. In this article, we propose a flexible embedding-based graph exploration pipeline to enjoy the best of both graph topology and node attributes. First, we leverage embedding algorithms for attributed graphs to encode the two perspectives into latent space. Then, we present an embedding-driven graph layout algorithm, GEGraph, which can achieve aesthetic layouts with better community preservation to support an easy interpretation of the graph structure. Next, graph explorations are extended based on the generated graph layout and insights extracted from the embedding vectors. Illustrated with examples, we build a layout-preserving aggregation method with Focus+Context interaction and a related nodes searching approach with multiple proximity strategies. Finally, we conduct quantitative and qualitative evaluations, a user study, and two case studies to validate our approach.

Sampling unknown large networks restricted by low sampling rates

Graph sampling plays an important role in data mining for large networks. Specifically, larger networks often correspond to lower sampling rates. Under the situation, traditional traversal-based samplings for large networks usually have an excessive preference for densely-connected network core nodes. Aim at this issue, this paper proposes a sampling method for unknown networks at low sampling rates, called SLSR, which first adopts a random node sampling to evaluate a degree threshold, utilized to distinguish the core from periphery, and the average degree in unknown networks, and then runs a double-layer sampling strategy on the core and periphery. SLSR is simple that results in a high time efficiency, but experiments verify that the proposed method can accurately preserve many critical structures of unknown large scale-free networks with low sampling rates and low variances.

Taurus: Towards a Unified Force Representation and Universal Solver for Graph Layout

Over the past few decades, a large number of graph layout techniques have been proposed for visualizing graphs from various domains. In this paper, we present a general framework, Taurus, for unifying popular techniques such as the spring-electrical model, stress model, and maxent-stress model. It is based on a unified force representation, which formulates most existing techniques as a combination of quotient-based forces that combine power functions of graph-theoretical and Euclidean distances. This representation enables us to compare the strengths and weaknesses of existing techniques, while facilitating the development of new methods. Based on this, we propose a new balanced stress model (BSM) that is able to layout graphs in superior quality. In addition, we introduce a universal augmented stochastic gradient descent (SGD) optimizer that efficiently finds proper solutions for all layout techniques. To demonstrate the power of our framework, we conduct a comprehensive evaluation of existing techniques on a large number of synthetic and real graphs. We release an open-source package, which facilitates easy comparison of different graph layout methods for any graph input as well as effectively creating customized graph layout techniques.

Evaluating Effects of Background Stories on Graph Perception

A graph is an abstract model that represents relations among entities, for example, the interactions between characters in a novel. A background story endows entities and relations with real-world meanings and describes the semantics and context of the abstract model, for example, the actual story that the novel presents. Considering practical experience and prior research, human viewers who are familiar with the background story of a graph and those who do not know the background story may perceive the same graph differently. However, no previous research has adequately addressed this problem. This research article thus presents an evaluation that investigated the effects of background stories on graph perception. Three hypotheses that focused on the role of visual focus areas, graph structure identification, and mental model formation on graph perception were formulated and guided three controlled experiments that evaluated the hypotheses using real-world graphs with background stories. An analysis of the resulting experimental data, which compared the performance of participants who read and did not read the background stories, obtained a set of instructive findings. First, having knowledge about a graph's background story influences participants' focus areas during interactive graph explorations. Second, such knowledge significantly affects one's ability to identify community structures but not high degree and bridge structures. Third, this knowledge influences graph recognition under blurred visual conditions. These findings can bring new considerations to the design of storytelling visualizations and interactive graph explorations.

Optimizing graph layout by t-SNE perplexity estimation

Perplexity is one of the key parameters of dimensionality reduction algorithm of t-distributed stochastic neighbor embedding (t-SNE). In this paper, we investigated the relationship of t-SNE perplexity and graph layout evaluation metrics including graph stress, preserved neighborhood information and visual inspection. As we found that a small perplexity is correlated with a relative higher normalized stress while preserving neighborhood information with a higher precision but less global structure information, we proposed our method to estimate appropriate perplexity either based on a modified standard t-SNE or the sklearn Barnes–Hut TSNE. Experimental results demonstrate effectiveness and ease of use of our approach when tested on a set of benchmark datasets.

Evaluating Representation Learning and Graph Layout Methods for Visualization

Graphs and other structured data have come to the forefront in machine learning over the past few years due to the efficacy of novel representation learning methods boosting the prediction performance in various tasks. Representation learning methods embed the nodes in a low-dimensional real-valued space, enabling the application of traditional machine learning methods on graphs. These representations have been widely premised to be also suited for graph visualization. However, no benchmarks or encompassing studies on this topic exist. We present an empirical study comparing several state-of-the-art representation learning methods with two recent graph layout algorithms, using readability and distance-based measures as well as the link prediction performance. Generally, no method consistently outperformed the others across quality measures. The graph layout methods provided qualitatively superior layouts when compared to representation learning methods. Embedding graphs in a higher dimensional space and applying t-distributed stochastic neighbor embedding for visualization improved the preservation of local neighborhoods, albeit at substantially higher computational cost.

Multivariate Network Layout Using Force-Directed Method with Attribute Constraints

Graph visualization with proper layout is widely applied to understand the relationship between entities in a complex system and the topological structure information is mainly used. Real-world graphs often have the community structures property which is ignored in many existing graph layout methods. Thus, we propose a multivariate network layout method using the force-directed method with attribute constraints. This method can effectively take into account the hierarchical structure, connection strength, and quantitative comparison between communities. First, the layout of community centers is generated by a force-directed algorithm in which node count of the community is taken as constraints to enable area balance of community; Second, community force based on node attribute is added in the force-directed algorithm to maintain the community clarity. A visualization system is also developed to allow users to interactively generate community structure-aware layout results. qualitative and quantitative evaluation of the results verifies the usability and effectiveness of the proposed method by comparing it with other methods.