Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Adjacency Matrices <s> In Web data, telecommunications traffic and in epidemiological studies, dense subgraphs correspond to subsets of subjects (i.e. users, patients) that share a collection of attributes values (i.e. accessed Web pages, email-calling patterns or disease diagnostic profiles). Visual and computational identification of these "clusters" becomes useful when domain experts desire to determine those factors of major influence in the formation of access and communication clusters or in the detection and contention of disease spread. With the current increases in graphic hardware capabilities and RAM sizes, it is more useful to relate graph sizes to the available screen real estate S and the amount of available RAM M, instead of the number of edges or nodes in the graph. We offer a visual interface that is parameterized by M and S and is particularly suited for navigation tasks that require the identification of subgraphs whose edge density is above certain threshold. This is achieved by providing a zoomable matrix view of the underlying data. This view is strongly coupled to a hierarchical view of the essential information elements present in the data domain. We illustrate the applicability of this work to the visual navigation of cancer incidence data and to an aggregated sample of phone call traffic <s> BIB001 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Adjacency Matrices <s> In this article, we describe a taxonomy of generic graph related tasks along with a computer-based evaluation designed to assess the readability of two representations of graphs: matrix-based representations and node-link diagrams. This evaluation encompasses seven generic tasks and leads to insightful recommendations for the representation of graphs according to their size and density. Typically, we show that when graphs are bigger than twenty vertices, the matrix-based visualization outperforms node-link diagrams on most tasks. Only path finding is consistently in favor of node-link diagrams throughout the evaluation. <s> BIB002 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Adjacency Matrices <s> MatrixExplorer is a network visualization system that uses two representations: node-link diagrams and matrices. Its design comes from a list of requirements formalized after several interviews and a participatory design session conducted with social science researchers. Although matrices are commonly used in social networks analysis, very few systems support the matrix-based representations to visualize and analyze networks. MatrixExplorer provides several novel features to support the exploration of social networks with a matrix-based representation, in addition to the standard interactive filtering and clustering functions. It provides tools to reorder (layout) matrices, to annotate and compare findings across different layouts and find consensus among several clusterings. MatrixExplorer also supports node-link diagram views which are familiar to most users and remain a convenient way to publish or communicate exploration results. Matrix and node-link representations are kept synchronized at all stages of the exploration process <s> BIB003 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Adjacency Matrices <s> The need to visualize large social networks is growing as hardware capabilities make analyzing large networks feasible and many new data sets become available. Unfortunately, the visualizations in existing systems do not satisfactorily resolve the basic dilemma of being readable both for the global structure of the network and also for detailed analysis of local communities. To address this problem, we present NodeTrix, a hybrid representation for networks that combines the advantages of two traditional representations: node-link diagrams are used to show the global structure of a network, while arbitrary portions of the network can be shown as adjacency matrices to better support the analysis of communities. A key contribution is a set of interaction techniques. These allow analysts to create a NodeTrix visualization by dragging selections to and from node-link and matrix forms, and to flexibly manipulate the NodeTrix representation to explore the dataset and create meaningful summary visualizations of their findings. Finally, we present a case study applying NodeTrix to the analysis of the InfoVis 2004 coauthorship dataset to illustrate the capabilities of NodeTrix as both an exploration tool and an effective means of communicating results. <s> BIB004 </s> Hierarchical Aggregation for Information Visualization: Overview, Techniques, and Design Guidelines <s> Adjacency Matrices <s> We present the zoomable adjacency matrix explorer (ZAME), a visualization tool for exploring graphs at a scale of millions of nodes and edges. ZAME is based on an adjacency matrix graph representation aggregated at multiple scales. It allows analysts to explore a graph at many levels, zooming and panning with interactive performance from an overview to the most detailed views. Several components work together in the ZAME tool to make this possible. Efficient matrix ordering algorithms group related elements. Individual data cases are aggregated into higher-order meta-representations. Aggregates are arranged into a pyramid hierarchy that allows for on-demand paging to GPU shader programs to support smooth multiscale browsing. Using ZAME, we are able to explore the entire French Wikipedia - over 500,000 articles and 6,000,000 links - with interactive performance on standard consumer-level computer hardware. <s> BIB005
Instead of explicitly drawing nodes and edges as graphical entries laid out on a visual substrate, adjacency matrices arrange nodes along the rows and columns of a matrix and represent edges between nodes as cells in the contents of the matrix. Adjacency matrices have been shown to be more efficient than node-link diagrams for large and/or dense graphs BIB002 , and are, thus, often employed for visualizing large graphs, either alone or in tandem BIB003 with node-link diagrams. The NodeTrix BIB004 technique mentioned in the previous section is an example of an aggregated hybrid between node-link and matrix representations. However, as noted above, the technique is not a true aggregated visualization due to its fixed aggregation structure. The Matrix Zoom BIB001 system, on the other hand, takes edge aggregation to its extreme by displaying large-scale graphs as a hierarchy of adjacency matrices given a predefined clustering hierarchy. Matrix Zoom uses animated transitions between levels in the aggregate hierarchy instead of supporting continuous zoom and pan interactions. Similarly, the Zoomable Adjacency Matrix Explorer (ZAME) BIB005 defines a pyramid of recursive edge merging where each level is half the dimension of the level below. Hence, each visual edge aggregate clusters four visual aggregates in the level below (Fig. 14) . This way, ZAME is able to visualize very large graphs of the order of 10 6 nodes and edges (Fig. 15) . Instead of fixed animations, like Matrix Zoom, the system implements many of the interaction techniques outlined in Section 3.5 of this paper such as zoom and pan, drill-down/roll-up, and coupled zoom and drill. In addition, the system also provides a rich set of visual representations for edge aggregates (Fig. 16 ) drawn using small programs (shaders) running on the graphics hardware.