A layout algorithm for undirected compound graphs

We present an algorithm for the layout of undirected compound graphs, relaxing restrictions of previously known algorithms in regards to topology and geometry. The algorithm is based on the traditional force-directed layout scheme with extensions to handle multi-level nesting, edges between nodes of arbitrary nesting levels, varying node sizes, and other possible application-specific constraints. Experimental results show that the execution time and quality of the produced drawings with respect to commonly accepted layout criteria are quite satisfactory. The algorithm has also been successfully implemented as part of a pathway integration and analysis toolkit named PATIKA, for drawing complicated biological pathways with compartmental constraints and arbitrary nesting relations to represent molecular complexes and various types of pathway abstractions.     

Visual exploration of complex time-varying graphs

Quasi-trees, namely graphs with tree-like structure, appear in many application domains, including bioinformatics and computer networks. Our new SPF approach exploits the structure of these graphs with a two-level approach to drawing, where the graph is decomposed into a tree of biconnected components. The low-level biconnected components are drawn with a force-directed approach that uses a spanning tree skeleton as a starting point for the layout. The higher-level structure of the graph is a true tree with meta-nodes of variable size that contain each biconnected component. That tree is drawn with a new area-aware variant of a tree drawing algorithm that handles high-degree nodes gracefully, at the cost of allowing edge-node overlaps. SPF performs an order of magnitude faster than the best previous approaches, while producing drawings of commensurate or improved quality     

SetCoLa: High‐Level Constraints for Graph Layout

Constraints enable flexible graph layout by combining the ease of automatic layout with customizations for a particular domain. However, constraint‐based layout often requires many individual constraints defined over specific nodes and node pairs. In addition to the effort of writing and maintaining a large number of similar constraints, such constraints are specific to the particular graph and thus cannot generalize to other graphs in the same domain. To facilitate the specification of customized and generalizable constraint layouts, we contribute SetCoLa: a domain‐specific language for specifying high‐level constraints relative to properties of the backing data. Users identify node sets based on data or graph properties and apply high‐level constraints within each set. Applying constraints to node sets rather than individual nodes reduces specification effort and facilitates reapplication of customized layouts across distinct graphs. We demonstrate the conciseness, generalizability, and expressiveness of SetCoLa on a series of real‐world examples from ecological networks, biological systems, and social networks.     

基于力导向模型的网络图自动布局算法综述

实现网络图形中节点和边自动布局一直是可视化研究中一个重要内容,基于力导向模型的自动布局算法则是该类研究中应用最广、文献最多的一类方法。根据研究方向出现的时间顺序,从基本模型、基于多维尺度分析的布局算法、多层迭代布局算法、非欧空间节点布局算法、受约束图形自动布局算法等五个方面对基于力引导模型的网络图自动布局算法的典型方法、研究进展、分支情况等进行了描述,并对发展前沿进行了讨论。     

Pathfinder: Visual Analysis of Paths in Graphs

The analysis of paths in graphs is highly relevant in many domains. Typically, path‐related tasks are performed in node‐link layouts. Unfortunately, graph layouts often do not scale to the size of many real world networks. Also, many networks are multivariate, i.e., contain rich attribute sets associated with the nodes and edges. These attributes are often critical in judging paths, but directly visualizing attributes in a graph layout exacerbates the scalability problem. In this paper, we present visual analysis solutions dedicated to path‐related tasks in large and highly multivariate graphs. We show that by focusing on paths, we can address the scalability problem of multivariate graph visualization, equipping analysts with a powerful tool to explore large graphs. We introduce Pathfinder, a technique that provides visual methods to query paths, while considering various constraints. The resulting set of paths is visualized in both a ranked list and as a node‐link diagram. For the paths in the list, we display rich attribute data associated with nodes and edges, and the node‐link diagram provides topological context. The paths can be ranked based on topological properties, such as path length or average node degree, and scores derived from attribute data. Pathfinder is designed to scale to graphs with tens of thousands of nodes and edges by employing strategies such as incremental query results. We demonstrate Pathfinder's fitness for use in scenarios with data from a coauthor network and biological pathways.     

一种支持超视频创建与可视呈现的草图界面技术

超视频打破了传统视频的单一线性的组织和浏览方式,有效地增强了用户的浏览效率和视频信息的表达能力.基于草图和草图界面在思维表达上的优势,针对目前对视频内容以及视频间或者视频内的关系展示上的不足,提出了一种支持超视频创建的草图界面来直观地表达用户的设计意图,改善了视频编辑过程中的交互体验.提出了一种基于force-directed 的图布局算法.该算法对视频语义进行建模,将时间、空间、视频结构、约束关系等语义信息融入到节点质量、引力和斥力等对象中.系统实例表明,该方法能够很好地适应视频特有的语义类型,表示出超视频的动态创建和编辑过程.     

基于社团划分的网络聚类布局算法

复杂网络日益受到广大专家和学者们的关注,对其进行可视化展示可以帮助用户发现复杂网络表征的复杂系统中隐藏的知识信息,对计算机科学、社会学、生物学等领域具有重要的意义。力导引布局算法是复杂网络可视化领域的主流算法,它用节点连接图的形式对复杂网络进行抽象表示,布局遵循一定的美学标准如节点的均匀分布、边长尽量一致等,这在一定程度上阻碍了对复杂网络的社团结构的展示。针对以上问题,本文提出引入基于度中心性的社团斥力与引力对力导引算法进行改进,以对复杂网络进行聚类布局。实验结果表明,本文算法可有效地展示复杂网络的社团结构,同时又能保留社团之间边缘节点的信息。     

A layout algorithm for signaling pathways

Visualization is crucial to the effective analysis of biological pathways. A poorly laid out pathway confuses the user, while a well laid out one improves the user’s comprehension of the underlying biological phenomenon.We present a new, elegant algorithm for layout of biological signaling pathways. Our algorithm uses a force-directed layout scheme, taking into account directional and rectangular regional constraints enforced by different molecular interaction types and subcellular locations in a cell. The algorithm has been successfully implemented as part of a pathway visualization and analysis toolkit named Patika, and results with respect to computational complexity and quality of the layout have been found satisfactory. The algorithm may be easily adapted to be used in other applications with similar conventions and constraints as well.Patika version 1.0 beta is available upon request at http://www.patika.org.     

Drawing directed graphs using quadratic programming

We describe a new method for visualization of directed graphs. The method combines constraint programming techniques with a high performance force-directed placement (FDP) algorithm. The resulting placements highlight hierarchy in directed graphs while retaining useful properties of FDP; such as emphasis of symmetries and preservation of proximity relations. Our algorithm automatically identifies those parts of the digraph that contain hierarchical information and draws them accordingly. Additionally, those parts that do not contain hierarchy are drawn at the same quality expected from a nonhierarchical, undirected layout algorithm. Our experiments show that this new approach is better able to convey the structure of large digraphs than the most widely used hierarchical graph-drawing method. An interesting application of our algorithm is directional multidimensional scaling (DMDS). DMDS deals with low-dimensional embedding of multivariate data where we want to emphasize the overall flow in the data (e.g., chronological progress) along one of the axes.     

Aesthetics-based Graph Layout for Human Consumption

Automatic graph layout is an important and long-studied problem. The basic straight-edge graph layout problem is to find spatial positions for the nodes of an input graph that maximize some measure of desirability. When graph layout is intended for human consumption, we call this measure of desirability an aesthetic. We seek an algorithm that produces graph layouts of high aesthetic quality not only for general graphs, but also for specific classes of graphs, such as trees and directed acyclic graphs. The Aesthetic Graph Layout (AGLO) approach described in this paper models graph layout as a multiobjective optimization problem, where the value of a layout is determined by multiple user-controlled layout aesthetics. The current AGLO algorithm combines the power and flexibility of the simulated annealing approach of Davidson and Harel (1989) with the relative speed of the method of Fruchterman and Reingold (1991). In addition, it is more general, and incorporates several new layout aesthetics to support new layout styles. Using these aesthetics, we are able to produce pleasing displays for graphs on which these other methods flounder.     

Non-Euclidean spring embedders

We present a conceptually simple approach to generalizing force-directed methods for graph layout from Euclidean geometry to Riemannian geometries. Unlike previous work on non-Euclidean force-directed methods, ours is not limited to special classes of graphs, but can be applied to arbitrary graphs. The method relies on extending the Euclidean notions of distance, angle, and force-interactions to smooth non-Euclidean geometries via projections to and from appropriately chosen tangent spaces. In particular, we formally describe the calculations needed to extend such algorithms to hyperbolic and spherical geometries. We also study the theoretical and practical considerations that arise when working with non-Euclidean geometries.     

基于核数分层的AS级网络拓扑可视化布局算法

分析了当前几种常见的网络拓扑布局算法,针对Internet自治域级网络拓扑结构的特征和发现现状,提出了一种核数分层的混合拓扑布局算法,在网络核心层采用力导向布局算法,在网络非核心层采用树型布局算法,较好地解决了节点合理布局问题和计算效率问题。实验证明该算法能够反映自治域网络的基本特征,布局清晰、直观,具有较强的可读性。     

Scalable, Versatile and Simple Constrained Graph Layout

We describe a new technique for graph layout subject to constraints. Compared to previous techniques the proposed method is much faster and scalable to much larger graphs. For a graph with n nodes, m edges and c constraints it computes incremental layout in time O ( n log n + m + c ) per iteration. Also, it supports a much more powerful class of constraint: inequalities or equalities over the Euclidean distance between nodes. We demonstrate the power of this technique by application to a number of diagramming conventions which previous constrained graph layout methods could not support. Further, the constraint-satisfaction method—inspired by recent work in position-based dynamics—is far simpler to implement than previous methods.     

一种用于Marching-Graph图形绘制的快速收敛布局算法

Marching-Graph是一种将图形隐喻技术和空间隐喻技术集成为一体的新的可视化方法.它为用户提供了高度可交互性地图,使用户可访问那些具有地理属性的信息的逻辑结构.它通过有效的人图交互和跨空间浏览为用户提供了一种可视分析和挖掘未知信息的机制,而不是将已知的信息呈现在地图上.然而,传统的力导向布局算法在达到力量均衡配置方面非常慢.为使一个图形布局收敛,它们通常需花费几十秒的时间.因此。当用户快速行进于地理区间时,那些力导向布局算法就不能满足快速绘制一系列图形的要求.提出了一种快速收敛布局方法,当用户在Marching-Graph中通过力导向布局逐步探究一系列图形时,它可以加速交互时间.通过结合辐射树绘图技术和力导向图形绘制方法来取得能量最小化的快速收敛.     

Inverse Markov Process Based Constrained Dynamic Graph Layout

In online dynamic graph drawing,constraints over nodes and node pairs help preserve a coherent mental map in a sequence of graphs.Defining the constraints is challenging due to the requirements of both preserving mental map and satisfying the visual aesthetics of a graph layout.Most existing algorithms basically depend on local changes but fail to do proper evaluations on the global propagation when setting constraints.To solve this problem,we introduce a heuristic model derived from PageRank which simulates the node movement as an inverse Markov process hence to give a global analysis of the layout's change,according to which different constraints can be set.These constraints,along with stress function,generate layouts maintaining spatial positions and shapes of relatively stable substructures between adjacent graphs.Experiments demonstrate that our method preserves both structure and position similarity to help users track graph changes visually.     

社交网络数据个性化推荐的可视化方法

针对大规模社交网络应用中检索结果过于庞大复杂的问题,将个性化推荐与可视化相结合,用于在大量数据中找到用户感兴趣的信息。在开拓网络缩放算法的基础上,提出关键信息显示算法,能够区别显示社交网络关系图中用户相对重要的信息和次要信息,增强关联度较高数据的显示效果。将带权值的力导向布局算法应用于用户关系聚类中,通过在二维显示空间中合理安排节点布局,达到减少用户认知负担和个性化推荐的目的。设计并实现个性化推荐的可视化工具HRVis,在Movielens数据集上进行测试,结果表明,HRVis能够强调显示具有良好社会关系的重要用户以及与用户相似的关联用户,获得较好的可视推荐效果。     

Finding overlapping communities in a complex network of social linkages and Internet of things

Online social networks play an important role in today’s Internet. These social networks contain huge amounts of data and the integrated framework of SN with Internet of things (IoT) presents a challenging problem. IoT is the ubiquitous interconnection of everyday items of interest (things), providing connectivity anytime, anywhere, and with anything. Like biological, co-authorship, and virus-spread networks, IoT and Social Network (SN) can be characterized to be complex networks containing substantial useful information. In the past few years, community detection in graphs has been an active area of research (Lee and Won in Proceedings of IEEE SoutheastCon, pp. 1–5, 2012). Many graph mining algorithms have been proposed, but none of them can help in capturing an important dimension of SNs, which is friendship. A friend circle expands with the help of mutual friends, and, thus, mutual friends play an important role in social networks’ growth. We propose two graph clustering algorithms: one for undirected graphs such as Facebook and Google+, and the other for directed graphs such as Twitter. The algorithms extract communities, and based on the access control policy nodes share resources (things). In the proposed Community Detection in Integrated IoT and SN (CDIISN) algorithm, we divide the nodes/actors of complex networks into basic, and IoT nodes. We, then, execute the community detection algorithm on them. We take nodes of a graph as members of a SN, and edges depicting the relations between the nodes. The CDIISN algorithm is purely deterministic, and no fuzzy communities are formed. It is known that one community detection algorithm is not suitable for all types of networks. For different network structures, different algorithms exhibit different results, and methods of execution. However, in our proposed method, the community detection algorithm can be modified as desired by a user based on the network connections. The proposed community detection approach is unique in the sense that a user can define his community detection criteria based on the kind of network.     

Node overlap removal in clustered directed acyclic graphs

Graph drawing and visualization represent structural information as diagrams of abstract graphs and networks. An important subset of graphs is directed acyclic graphs (DAGs). This paper presents a new E-Spring algorithm, extended from the popular spring embedder model, which eliminates node overlaps in clustered DAGs. In this framework, nodes are modeled as non-uniform charged particles with weights, and a final drawing is derived by adjusting the positions of the nodes according to a combination of spring forces and repulsive forces derived from electrostatic forces between the nodes. The drawing process needs to reach a stable state when the average distances of separation between nodes are near optimal. We introduce a stopping condition for such a stable state, which reduces equilibrium distances between nodes and therefore results in a significantly reduced area for DAG visualization. It imposes an upper bound on the repulsive forces between nodes based on graph geometry. The algorithm employs node interleaving to eliminate any residual node overlaps. These new techniques have been validated by visualizing eBay buyer–seller relationships and has resulted in overall area reductions in the range of 45–79%.     

Deterministic broadcasting in ad hoc radio networks

We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and node u either hears the noise of interference of messages, enabling it to detect a collision, or does not hear anything at all, depending on the model. We assume that nodes know neither the topology nor the size of the network, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. Such networks are called ad hoc multi-hop networks. We study the time of deterministic broadcasting under this scenario. For the model without collision detection, we develop a linear-time broadcasting algorithm for symmetric graphs, which is optimal, and an algorithm for arbitrary n-node graphs, working in time . Next we show that broadcasting with acknowledgement is not possible in this model at all. For the model with collision detection, we develop efficient algorithms for broadcasting and for acknowledged broadcasting in strongly connected graphs. Received: January 2000 / Accepted: June 2001