Recherche et représentation de communautés dans des grands graphes

15 pagesNational audienceThis paper deals with the analysis and the visualization of large graphs. Our interest in such a subject-matter is related to the fact that graphs are convenient widespread data structures. Indeed, this type of data can be encountered in a growing number of concrete problems: Web, information retrieval, social networks, biological interaction networks... Furthermore, the size of these graphs becomes increasingly large as the progression of the means for data gathering and storage steadily strengthens. This calls for new methods in graph analysis and visualization which are now important and dynamic research fields at the interface of many disciplines such as mathematics, statistics, computer science and sociology. In this paper, we propose a method for graphs representation and visualization based on a prior clustering of the vertices. Newman and Girvan (2004) points out that “reducing [the] level of complexity [of a network] to one that can be interpreted readily by the human eye, will be invaluable in helping us to understand the large-scale structure of these new network data”: we rely on this assumption to use a priori a clustering of the vertices as a preliminary step for simplifying the representation of the graphs - as a whole. The clustering phase consists in optimizing a quality measure specifically suitable for the research of dense groups in graphs. This quality measure is the modularity and expresses the “distance” to a null model in which the graph edges do not depend on the clustering. The modularity has shown its relevance in solving the problem of uncovering dense groups in a graph. Optimization of the modularity is done through a stochastic simulated annealing algorithm. The visualization/representation phase, as such, is based on a force-directed algorithm described in Truong et al. (2007). After giving a short introduction to the problem and detailing the vertices clustering and representation algorithms, the paper will introduce and discuss two applications from the social network field

An energy-based model to optimize cluster visualization

National audienceGraphs are mathematical structures that provide natural means for complex-data representation. Graphs capture the structure and thus help modeling a wide range of complex real-life data in various domains. Moreover graphs are especially suitable for information visualization. Indeed the intuitive visualabstraction (dots and lines) they provide is intimately associated with graphs. Visualization paves the way to interactive exploratory data-analysis and to important goals such as identifying groups and subgroups among data and helping to understand how these groups interact with each other. In this paper, we present a graph drawing approach that helps to better appreciate the cluster structure in data and the interactions that may exist between clusters. In this work, we assume that the clusters are already extracted and focus rather on the visualization aspects. We propose an energy-based model for graph drawing that produces an esthetic drawing that ensures each cluster will occupy a separate zone within thevisualization layout. This method emphasizes the inter-groups interactions and still shows the inter-nodes interactions. The drawing areas assigned to the clusters can be user-specified (prefixed areas) or automatically crafted (free areas). The approach we suggest also enables handling geographically-based clustering. In the case of free areas, we illustrate the use of our drawing method through an example. In the case of prefixed areas, we firstuse an example from citation networks and then use another exampleto compare the results of our method to those of the divide and conquer approach. In the latter case, we show that while the two methods successfully point out the cluster structure our method better visualize the global structure

An Empirical Evaluation of Force-Directed Graph Layout

Force-directed graph layout is a widely used algorithm for the automatic layout of graphs. Little experimental work has been done exploring the behaviour of the algorithm under a variety of conditions. This thesis carries out three large-scale metric-based experiments. The first explores how the core algorithm behaves under changes to initial conditions. The second looks at extending the force-directed layout algorithm with additional forces to reduce overlaps. The third develops a novel symmetry metric for graphs and uses that to explore the symmetries of graphs. This thesis also carries out a user study to show that the differences reported by metrics in the graphs are reflected in a difference in user performance when using graphs for a free-form selection task

DEPLOYING, IMPROVING AND EVALUATING EDGE BUNDLING METHODS FOR VISUALIZING LARGE GRAPHS

A tremendous increase in the scale of graphs has been witnessed in a wide range of fields, which demands efficient and effective visualization techniques to assist users in better understandings of large graphs. Conventional node-link diagrams are often used to visualize graphs, whereas excessive edge crossings can easily incur severe visual clutter in the node-link diagram of a large graph. Edge bundling can effectively remedy visual clutter and reveal high-level graph structures. Although significant efforts have been devoted to developing edge bundling, three challenging problems remain. First, edge bundling techniques are often computationally expensive and are not easy to deploy for web-based applications. The state-of-the-art edge bundling methods often require special system supports and techniques such as high-end GPU acceleration for large graphs, which makes these methods less portable, especially for ubiquitous mobile devices. Second, the quantitative quality of edge bundling results is barely assessed in the literature. Currently, the comparison of edge bundling mainly focuses on computational performance and perceptual results. Third, although the family of edge bundling techniques has a rich set of bundling layout, there is a lack of a generic method to generate different styles of edge bundling. In this research, I aim to address these problems and have made the following contributions. First, I provide an efficient framework to deploy edge bundling for web-based platforms by exploiting standard graphics hardware functions and libraries. My framework can generate high-quality edge bundling results on web-based platforms, and achieve a speedup of 50X compared to the previous state-of-the-art edge bundling method on a graph with half of a million edges. Second, I propose a new moving least squares based approach to lower the algorithm complexity of edge bundling. In addition, my approach can generate better bundling results compared to other methods based on a quality metric. Third, I provide an information-theoretic metric to evaluate the edge bundling methods. I leverage information theory in this metric. With my information-theoretic metric, domain users can choose appropriate edge bundling methods with proper parameters for their applications. Last but not least, I present a deep learning framework for edge bundling visualizations. Through a training process that learns the results of a specific edge bundling method, my deep learning framework can infer the final layout of the edge bundling method. My deep learning framework is a generic framework that can generate the corresponding results of different edge bundling methods. Adviser: Hongfeng Y

Drawing graphs with nonuniform nodes using potential fields

Abstract. A potential field approach, coupled with force-directed methods, is proposed in this paper for drawing graphs with nonuniform nodes in 2-D and 3-D. In our framework, nonuniform nodes are uniformly or nonuniformly charged, while edges are modelled by springs. Using certain techniques developed in the field of potential-based path planning, we are able to find analytically tractable procedures for computing the repulsive force and torque of a node in the potential field induced by the remaining nodes. Our experimental results suggest this new approach to be promising, as drawings of good quality for a variety of graphs in 2-D and 3-D can be produced efficiently.

A Potential-Field-Based Multilevel Algorithm for Drawing Large Graphs

The aim of automatic graph drawing is to compute a well-readable layout of a given graph G=(V,E). One very popular class of algorithms for drawing general graphs are force-directed methods. These methods generate drawings of G in the plane so that each edge is represented by a straight line connecting its two adjacent nodes. The computation of the drawings is based on associating G with a physical model. Then, the algorithms iteratively try to find a placement of the nodes so that the total energy of the physical system is minimal. Several force-directed methods can visualize large graphs containing many thousands of vertices in reasonable time. However, only some of these methods guarantee a sub-quadratic running time in special cases or under certain assumptions, but not in general. The others are not sub-quadratic at all. We develop a new force-directed algorithm that is based on a combination of an efficient multilevel strategy and a method for approximating the repulsive forces in the system by rapidly evaluating potential fields. The worst-case running time of the new method is O(|V| log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs containing up to 100000 nodes in less than five minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for other tested methods