Force-Directed Edge Bundling for Graph Visualization

Graphs depicted as node-link diagrams are widely used to show relationships between entities. However, node-link diagrams comprised of a large number of nodes and edges often suffer from visual clutter. The use of edge bundling remedies this and reveals high-level edge patterns. Previous methods require the graph to contain a hierarchy for this, or they construct a control mesh to guide the edge bundling process, which often results in bundles that show considerable variation in curvature along the overall bundle direction. We present a new edge bundling method that uses a self-organizing approach to bundling in which edges are modeled as flexible springs that can attract each other. In contrast to previous methods, no hierarchy is used and no control mesh. The resulting bundled graphs show significant clutter reduction and clearly visible high-level edge patterns. Curvature variation is furthermore minimized, resulting in smooth bundles that are easy to follow. Finally, we present a rendering technique that can be used to emphasize the bundling.     

Hierarchical edge bundles: visualization of adjacency relations in hierarchical data

A compound graph is a frequently encountered type of data set. Relations are given between items, and a hierarchy is defined on the items as well. We present a new method for visualizing such compound graphs. Our approach is based on visually bundling the adjacency edges, i.e., non-hierarchical edges, together. We realize this as follows. We assume that the hierarchy is shown via a standard tree visualization method. Next, we bend each adjacency edge, modeled as a B-spline curve, toward the polyline defined by the path via the inclusion edges from one node to another. This hierarchical bundling reduces visual clutter and also visualizes implicit adjacency edges between parent nodes that are the result of explicit adjacency edges between their respective child nodes. Furthermore, hierarchical edge bundling is a generic method which can be used in conjunction with existing tree visualization techniques. We illustrate our technique by providing example visualizations and discuss the results based on an informal evaluation provided by potential users of such visualizations     

Divided edge bundling for directional network data

The node-link diagram is an intuitive and venerable way to depict a graph. To reduce clutter and improve the readability of node-link views, Holten & van Wijk's force-directed edge bundling employs a physical simulation to spatially group graph edges. While both useful and aesthetic, this technique has shortcomings: it bundles spatially proximal edges regardless of direction, weight, or graph connectivity. As a result, high-level directional edge patterns are obscured. We present divided edge bundling to tackle these shortcomings. By modifying the forces in the physical simulation, directional lanes appear as an emergent property of edge direction. By considering graph topology, we only bundle edges related by graph structure. Finally, we aggregate edge weights in bundles to enable more accurate visualization of total bundle weights. We compare visualizations created using our technique to standard force-directed edge bundling, matrix diagrams, and clustered graphs; we find that divided edge bundling leads to visualizations that are easier to interpret and reveal both familiar and previously obscured patterns.     

Convergent drawing for mutually connected directed graphs

Directed graphs are used to represent a variety of datasets, including friendship on social networking services (SNS), pathways of genes, and citations of research papers. Graph drawing is useful in representing such datasets. At the international conference on Information Visualization (IV), we have presented a convergent edge drawing and a node layout technique for tightly and mutually connected directed graphs. The edge drawing technique in the IV paper includes three features: ordinary bundling of edges connecting pairs of node clusters, convergence of multiple bundles that connect to the same node cluster, and shape adjustment of two bundles connecting the same pair of node clusters. In this paper, we present improved node layout and edge drawing techniques, which make our edge bundling more effective. This paper also introduces a case study with a directed paper citation graph dataset.vvvvv     

一种基于空间距离的边绑定方法

边绑定方法是近年来信息可视化领域的一个研究热点,解决图可视化中由于边的 过多交叉而引起的视觉混乱问题。在现有的边绑定方法中,基于路径构建的算法通常能够在时 间和绑定效果上获得较好的结果,其中基于边聚类和骨架构建路径的方法具有良好的数据表达 能力。在此基础上,提出一种基于空间距离的边绑定的方法,结合边的空间距离和骨架生成的 特点,在实现边绑定功能的同时针对以往基于骨架路径的方法做了进一步的改进。实验结果表 明,该方法相比原方法有着更高的时间效率,对数据的细节保留更为合理,消除了原方法存在 的绑定过度的问题,简化原方法的计算过程,并避免奇异性问题,更为实用。     

Image‐Based Edge Bundles: Simplified Visualization of Large Graphs

We present a new approach aimed at understanding the structure of connections in edge‐bundling layouts. We combine the advantages of edge bundles with a bundle‐centric simplified visual representation of a graph's structure. For this, we first compute a hierarchical edge clustering of a given graph layout which groups similar edges together. Next, we render clusters at a user‐selected level of detail using a new image‐based technique that combines distance‐based splatting and shape skeletonization. The overall result displays a given graph as a small set of overlapping shaded edge bundles. Luminance, saturation, hue, and shading encode edge density, edge types, and edge similarity. Finally, we add brushing and a new type of semantic lens to help navigation where local structures overlap. We illustrate the proposed method on several real‐world graph datasets.     

基于不确定使用边的间接依赖过滤方法

起源过滤是通过改造起源图中的节点、边或间接依赖关系,隐藏起源图中的敏感信息,实现起源安全发布的新兴技术.针对现有起源过滤研究主要关注节点和边的过滤,较少研究间接依赖的过滤问题.扩展现有"删除+修复"的间接依赖过滤策略,提出了一种起源间接依赖过滤方法.形式地定义不确定的使用边,并阐明引入不确定的使用边修复被误断的间接依赖...     

Visual Clustering in Parallel Coordinates

Parallel coordinates have been widely applied to visualize high‐dimensional and multivariate data, discerning patterns within the data through visual clustering. However, the effectiveness of this technique on large data is reduced by edge clutter. In this paper, we present a novel framework to reduce edge clutter, consequently improving the effectiveness of visual clustering. We exploit curved edges and optimize the arrangement of these curved edges by minimizing their curvature and maximizing the parallelism of adjacent edges. The overall visual clustering is improved by adjusting the shape of the edges while keeping their relative order. The experiments on several representative datasets demonstrate the effectiveness of our approach.     

Visual Inspection of Multivariate Graphs

Most graph visualization techniques focus on the structure of graphs and do not offer support for dealing with node attributes and edge labels. To enable users to detect relations and patterns in terms of data associated with nodes and edges, we present a technique where this data plays a more central role. Nodes and edges are clustered based on associated data. Via direct manipulation users can interactively inspect and query the graph. Questions that can be answered include, “which edge types are activated by specific node attributes?” and, “how and from where can I reach specific types of nodes?” To validate our approach we contrast it with current practice. We also provide several examples where our method was used to study transition graphs that model real‐world systems.     

Centrality Based Visualization of Small World Graphs

Current graph drawing algorithms enable the creation of two dimensional node‐link diagrams of huge graphs. However, for graphs with low diameter (of which “small world” graphs are a subset) these techniques begin to break down visually even when the graph has only a few hundred nodes. Typical algorithms produce images where nodes clump together in the center of the screen, making it hard to discern structure and follow paths. This paper describes a solution to this problem, which uses a global edge metric to determine a subset of edges that capture the graph's intrinsic clustering structure. This structure is then used to create an embedding of the graph, after which the remaining edges are added back in. We demonstrate applications of this technique to a number of real world examples.     

Visual Analysis of Sentiment and Information Spread on Micro-Blog

In this paper, we combined temporal analysis and spatial analysis together, and proposed the Electron Cloud Model (ECM) which is based on the Schrodinger equation and Niels Bohr atomic theory. The ECM is used to conduct temporal visual analysis of micro-blog sentiments. In the ECM, we made an attempt to mapping a score of sentiment to the electron stability and took neutral sentiments into consideration. We applied kernel density estimation and edge bundling to conduct space-varying visual analysis of sentiment. Kernel density estimation visualized sentiment changes in different levels of detail naturally while edge bundling was used to reduce visual clutter of edge crossing and reveal high-level edge patterns. Finally, we implemented an analysis system, conducted three case studies and made simple comparisons with other visualize methods.     

基于边密度聚类的重叠社区发现算法

基于边聚类的社区发现算法以边为聚类对象,自然发现重叠社区,但也存在生成的社区集边界归属模糊、社区结构过度重叠等问题.基于此种情况,文中提出基于边密度聚类的重叠社区发现算法.首先,以边为研究对象,通过密度聚类检测连接紧密的核心边社区.然后,根据边界边归属策略将边界边划分到离它最近的核心边社区.针对孤立边,提出基于边的度与边的社区归属的孤立边处理策略,进一步处理未划分的孤立边,避免社区结构过度重叠的问题.最后,将边社区还原为节点社区,实现重叠社区的发现.在人工数据集和真实数据集上的实验表明,文中算法可以快速准确地检测复杂网络中的重叠社区.     

Visualizing a Sequence of a Thousand Graphs (or Even More)

The visualization of dynamic graphs demands visually encoding at least three major data dimensions: vertices, edges, and time steps. Many of the state‐of‐the‐art techniques can show an overview of vertices and edges but lack a data‐scalable visual representation of the time aspect. In this paper, we address the problem of displaying dynamic graphs with a thousand or more time steps. Our proposed interleaved parallel edge splatting technique uses a time‐to‐space mapping and shows the complete dynamic graph in a static visualization. It provides an overview of all data dimensions, allowing for visually detecting time‐varying data patterns; hence, it serves as a starting point for further data exploration. By applying clustering and ordering techniques on the vertices, edge splatting on the links, and a dense time‐to‐space mapping, our approach becomes visually scalable in all three dynamic graph data dimensions. We illustrate the usefulness of our technique by applying it to call graphs and US domestic flight data with several hundred vertices, several thousand edges, and more than a thousand time steps.     

Faster Edge-Path Bundling through Graph Spanners

Edge-Path bundling is a recent edge bundling approach that does not incur ambiguities caused by bundling disconnected edges together. Although the approach produces less ambiguous bundlings, it suffers from high computational cost. In this paper, we present a new Edge-Path bundling approach that increases the computational speed of the algorithm without reducing the quality of the bundling. First, we demonstrate that biconnected components can be processed separately in an Edge-Path bundling of a graph without changing the result. Then, we present a new edge bundling algorithm that is based on observing and exploiting a strong relationship between Edge-Path bundling and graph spanners. Although the worst case complexity of the approach is the same as of the original Edge-Path bundling algorithm, we conduct experiments to demonstrate that the new approach is 5 – 256 times faster than Edge-Path bundling depending on the dataset, which brings its practical running time more in line with traditional edge bundling algorithms.     

Stochastic graph as a model for social networks

Social networks are usually modeled and represented as deterministic graphs with a set of nodes as users and edges as connection between users of networks. Due to the uncertain and dynamic nature of user behavior and human activities in social networks, their structural and behavioral parameters are time varying parameters and for this reason using deterministic graphs for modeling and analysis of behavior of users may not be appropriate. In this paper, we propose that stochastic graphs, in which weights associated with edges are random variables, may be a better candidate as a graph model for social network analysis. Thus, we first propose generalization of some network measures for stochastic graphs and then propose six learning automata based algorithms for calculating these measures under the situation that the probability distribution functions of the edge weights of the graph are unknown. Simulations on different synthetic stochastic graphs for calculating the network measures using the proposed algorithms show that in order to obtain good estimates for the network measures, the required number of samples taken from edges of the graph is significantly lower than that of standard sampling method aims to analysis of human behavior in online social networks.     

基于负数据库的隐私保护图神经网络推荐系统

图数据是一种特殊的数据形式,由节点和边组成.在这种数据中,实体被建模为节点,节点之间可能存在边,表示实体之间的关系.通过分析和挖掘这些数据,人们可以获得很多有价值的信息.因此,对于图中各个节点来说,它也带来了隐私信息泄露的风险.为了解决这个问题,本文提出了一种基于负数据库(NDB)的图数据发布方法.该方法将图数据的结构特征转换为负数据库的编码形式,基于此设计出一种扰动图(NDB-Graph)的生成方法,由于NDB是一种保护隐私的技术,不显式存储原始数据且难以逆转.故发布的图数据能确保原始图数据的安全.此外,由于图神经网络在图数据中关系特征处理方面的高效性,被广泛应用于对图数据的各种任务处理建模,例如推荐系统,本文还提出了一种基于NDB技术的图神经网络的推荐系统,来保护每个用户的图数据隐私.基于Karate和Facebook数据集上的实验表明,与PBCN发布方法相比,本文的方法在大多数情况下表现更优秀,例如,在Facebook数据集上,度分布最小的L1误差仅为6,比同隐私等级下的PBCN方法低约2.6%,最坏情况约为1400,比同隐私等级下PBCN方法低约46.5%.在基于LightGCN的协同过滤实验中,也表明所提出的隐私保护方法具有较高的精度.     

Unfolding Edges: Adding Context to Edges in Multivariate Graph Visualization

Existing work on visualizing multivariate graphs is primarily concerned with representing the attributes of nodes. Even though edges are the constitutive elements of networks, there have been only few attempts to visualize attributes of edges. In this work, we focus on the critical importance of edge attributes for interpreting network visualizations and building trust in the underlying data. We propose ‘unfolding of edges’ as an interactive approach to integrate multivariate edge attributes dynamically into existing node-link diagrams. Unfolding edges is an in-situ approach that gradually transforms basic links into detailed representations of the associated edge attributes. This approach extends focus+context, semantic zoom, and animated transitions for network visualizations to accommodate edge details on-demand without cluttering the overall graph layout. We explore the design space for the unfolding of edges, which covers aspects of making space for the unfolding, of actually representing the edge context, and of navigating between edges. To demonstrate the utility of our approach, we present two case studies in the context of historical network analysis and computational social science. For these, web-based prototypes were implemented based on which we conducted interviews with domain experts. The experts' feedback suggests that the proposed unfolding of edges is a useful tool for exploring rich edge information of multivariate graphs.     

Estimating graph distance and centrality on shared nothing architectures

We present a parallel toolkit for pairwise distance computation in massive networks. Computing the exact shortest paths between a large number of vertices is a costly operation, and serial algorithms are not practical for billion‐scale graphs. We first describe an efficient parallel method to solve the single source shortest path problem on commodity hardware with no shared memory. Using it as a building block, we introduce a new parallel algorithm to estimate the shortest paths between arbitrary pairs of vertices. Our method exploits data locality, produces highly accurate results, and allows batch computation of shortest paths with 7% average error in graphs that contain billions of edges. The proposed algorithm is up to two orders of magnitude faster than previously suggested algorithms and does not require large amounts of memory or expensive high‐end servers. We further leverage this method to estimate the closeness and betweenness centrality metrics, which involve systems challenges dealing with indexing, joining, and comparing large datasets efficiently. In one experiment, we mined a real‐world Web graph with 700 million nodes and 12 billion edges to identify the most central vertices and calculated more than 63 billion shortest paths in 6 h on a 20‐node commodity cluster. Copyright © 2014 John Wiley & Sons, Ltd.     

SEDMI: Saliency based edge detection in multispectral images

Detecting edges in multispectral images is difficult because different spectral bands may contain different edges. Existing approaches calculate the edge strength of a pixel locally, based on the variation in intensity between this pixel and its neighbors. Thus, they often fail to detect the edges of objects embedded in background clutter or objects which appear in only some of the bands.We propose SEDMI, a method that aims to overcome this problem by considering the salient properties of edges in an image. Based on the observation that edges are rare events in the image, we recast the problem of edge detection into the problem of detecting events that have a small probability in a newly defined feature space. The feature space is constructed by the spatial gradient magnitude in all spectral channels. As edges are often confined to small, isolated clusters in this feature space, the edge strength of a pixel, or the confidence value that this pixel is an event with a small probability, can be calculated based on the size of the cluster to which it belongs.Experimental results on a number of multispectral data sets and a comparison with other methods demonstrate the robustness of the proposed method in detecting objects embedded in background clutter or appearing only in a few bands.