Analyzing large, multivariate graphs is an important problem in many domains, yet such graphs are challenging to visualize. In this paper, we introduce a novel, scalable, tree-table multivariate graph visualization technique, which makes many tasks related to multivariate graph analysis easier to achieve. The core principle we follow is to selectively query for nodes or subgraphs of interest and visualize these subgraphs as a spanning tree of the graph. The tree is laid out linearly, which enables us to juxtapose the nodes with a table visualization where diverse attributes can be shown. We also use this table as an adjacency matrix, so that the resulting technique is a hybrid node-link adjacency matrix technique. We implement this concept in Juniper and complement it with a set of interaction techniques that enable analysts to dynamically grow, restructure, and aggregate the tree, as well as change the layout or show paths between nodes. We demonstrate the utility of our tool in usage scenarios for different multivariate networks: a bipartite network of scholars, papers, and citation metrics and a multitype network of story characters, places, books, etc.
have both favorable and unfavorable properties compared to node-link layouts when judging topology @cite_52 . Various attempts have been made to combine node-link layouts with matrices to find a compromise between these trade-offs. Examples are NodeTrix @cite_26 , which embeds adjacency matrices for subgraphs of a node-link layout, and MatLink @cite_22 , which enhances matrices with links. For attribute visualization, however, adjacency matrices are superior to node-link diagrams. For example, adjacency matrices can naturally encode edge attributes in matrix cells. Although this is mostly done with a single color value, multiple edge attributes can be visualized as nested graphs @cite_25 . Similar to the on-node encoding in node-link diagrams, however, the small space available for a matrix cell limits how much can be encoded. For node attributes, in contrast, it is easy to juxtapose multiple attribute visualizations with the rows or columns of the matrix. This has been done, for example in Graffinity @cite_10 and in MapTrix @cite_14 .
@cite_26 @cite_14 @cite_22 @cite_52 @cite_10 @cite_25
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Many real-world domains can be represented as large node-link graphs: backbone Internet routers connect with 70,000 other hosts, mid-sized Web servers handle between 20,000 and 200,000 hyperlinked documents, and dictionaries contain millions of words defined in terms of each other. Computational manipulation of such large graphs is common, but previous tools for graph visualization have been limited to datasets of a few thousand nodes. Visual depictions of graphs and networks are external representations that exploit human visual processing to reduce the cognitive load of many tasks that require understanding of global or local structure. We assert that the two key advantages of computer-based systems for information visualization over traditional paper-based visual exposition are interactivity and scalability. We also argue that designing visualization software by taking the characteristics of a target user's task domain into account leads to systems that are more effective and scale to larger datasets than previous work. This thesis contains a detailed analysis of three specialized systems for the interactive exploration of large graphs, relating the intended tasks to the spatial layout and visual encoding choices. We present two novel algorithms for specialized layout and drawing that use quite different visual metaphors. The H3 system for visualizing the hyperlink structures of web sites scales to datasets of over 100,000 nodes by using a carefully chosen spanning tree as the layout backbone, 3D hyperbolic geometry for a Focus+Context view, and provides a fluid interactive experience through guaranteed frame rate drawing. The Constellation system features a highly specialized 2D layout intended to spatially encode domain-specific information for computational linguists checking the plausibility of a large semantic network created from dictionaries. The Planet Multicast system for displaying the tunnel topology of the Internet's multicast backbone provides a literal 3D geographic layout of arcs on a globe to help MBone maintainers find misconfigured long-distance tunnels. Each of these three systems provides a very different view of the graph structure, and we evaluate their efficacy for the intended task. We generalize these findings in our analysis of the importance of interactivity and specialization for graph visualization systems that are effective and scalable. We apply adjacency matrix clustering to network attack graphs for attack correlation, prediction, and hypothesizing. We self-multiply the clustered adjacency matrices to show attacker reachability across the network for a given number of attack steps, culminating in transitive closure for attack prediction over all possible number of steps. This reachability analysis provides a concise summary of the impact of network configuration changes on the attack graph. Using our framework, we also place intrusion alarms in the context of vulnerability-based attack graphs, so that false alarms become apparent and missed detections can be inferred. We introduce a graphical technique that shows multiple-step attacks by matching rows and columns of the clustered adjacency matrix. This allows attack impact responses to be identified and prioritized according to the number of attack steps to victim machines, and allows attack origins to be determined. Our techniques have quadratic complexity in the size of the attack graph Visualizing social networks presents challeges for both node-link and adjacency matrix representations. Social networks are locally dense, which makes node-link displays unreadable. Yet, main analysis tasks require following paths, which is difficult on matrices. This article presents MatLink, a hybrid representation with links overlaid on the borders of a matrix and dynamic topological feedback as the pointer moves. We evaluated MatLink by an experiment comparing its readability, in term of errors and time, for social network-related tasks to the other conventional representations on graphs varying in size (small and medium) and density. It showed significant advantages for most tasks, especially path-related ones where standard matrices are weak. Motivation: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degree distribution, clustering coefficient, diameter, and relative graphlet frequency distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it is that the networks will truly be similar. Results: We introduce a new systematic measure of a network's local structure that imposes a large number of similarity constraints on networks being compared. In particular, we generalize the degree distribution, which measures the number of nodes 'touching' k edges, into distributions measuring the number of nodes 'touching' k graphlets, where graphlets are small connected non-isomorphic subgraphs of a large network. Our new measure of network local structure consists of 73 graphlet degree distributions of graphlets with 2--5 nodes, but it is easily extendible to a greater number of constraints (i.e. graphlets), if necessary, and the extensions are limited only by the available CPU. Furthermore, we show a way to combine the 73 graphlet degree distributions into a network 'agreement' measure which is a number between 0 and 1, where 1 means that networks have identical distributions and 0 means that they are far apart. Based on this new network agreement measure, we show that almost all of the 14 eukaryotic PPI networks, including human, resulting from various high-throughput experimental techniques, as well as from curated databases, are better modeled by geometric random graphs than by Erdos--Reny, random scale-free, or Barabasi--Albert scale-free networks. Availability: Software executables are available upon request. Contact: natasha@ics.uci.edu