In this paper, we present a new approach to exploring dynamic graphs. We have developed a new clustering algorithm for dynamic graphs which finds an ideal clustering for each time-step and links the clusters together. The resulting time-varying clusters are then used to define two visual representations. The first view is an overview that shows how clusters evolve over time and provides an interface to find and select interesting time-steps. The second view consists of a node link diagram of a selected time-step which uses the clustering to efficiently define the layout. By using the time-dependant clustering, we ensure the stability of our visualization and preserve user mental map by minimizing node motion, while simultaneously producing an ideal layout for each time step. Also, as the clustering is computed ahead of time, the second view updates in linear time which allows for interactivity even for graphs with upwards of tens of thousands of nodes.

The emergence of very large hierarchies that result from the increase in available data raises many problems of visualization and navigation. On data sets of such scale, classical graph drawing methods do not take advantage of certain human cognitive skills such as shape recognition. These cognitive skills could make it easier to remember the global structure of the data. In this paper, we propose a method that is based on the use of nested irregular shapes. We name it GosperMap as we rely on the use of a Gosper Curve to generate these shapes. By employing human perception mechanisms that were developed by handling, for example, cartographic maps, this technique facilitates the visualization and navigation of a hierarchy. An algorithm has been designed to preserve region containment according to the hierarchy and to set the leaves' sizes proportionally to a property, in such a way that the size of nonleaf regions corresponds to the sum of their children's sizes. Moreover, the input ordering of the hierarchy's nodes is preserved, i.e., the areas that represent two consecutive children of a node in the hierarchy are adjacent to one another. This property is especially useful because it guarantees some stability in our algorithm. We illustrate our technique by providing visualization examples of the repartition of tax money in the US over time. Furthermore, we validate the use of the GosperMap in a professional documentation context and show the stability and ease of memorization for this type of map.

Recent interest in complex systems and specially social networks has catalyzed the development of numerous models to help understand these networks. A number of models have been proposed recently where they are either variants of the small-world model, the preferential attachment model or both. Three fundamental properties attributed to identify these complex networks are high clustering coefficient, small average path length and the vertex connectivity following power-law distribution. Different models have been presented to generate networks having all these properties.In this paper, we focus on social networks and another important characteristic of these networks, which is the presence of Community Structures. Often misinterpret with the metric called clustering coefficient, we first show that the presence of Community Structures is indeed different from having high clustering coefficient. We then define a new network generation model which exhibits all the fundamental properties of complex networks along with the presence of Community Structures.

The problem of local community detection in graphs refers to the identification of a community that is specific to a query node and relies on limited information about the network structure. Existing approaches for this problem are defined to work in dynamic network scenarios, however they are not designed to deal with complex real-world networks, in which multiple types of connectivity might be considered. In this work, we fill this gap in the literature by introducing the first framework for local community detection in multilayer networks (ML-LCD). We formalize the ML-LCD optimization problem and provide three definitions of the associated objective function, which correspond to different ways to incorporate within-layer and across-layer topological features. We also exploit our framework to generate multilayer global community structures. We conduct an extensive experimentation using seven real-world multilayer networks, which also includes comparison with state-ofthe-art methods for single-layer local community detection and for multilayer global community detection. Results show the significance of our proposed methods in discovering local communities over multiple layers, and also highlight their ability in producing global community structures that are better in modularity than those produced by native global community detection approaches.