Social networks are the fabric of society and the subject of frequent visual analysis. Closed triads represent triangular relationships between three people in a social network and are significant for understanding in...
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ISBN:
(纸本)9798350393811;9798350393804
Social networks are the fabric of society and the subject of frequent visual analysis. Closed triads represent triangular relationships between three people in a social network and are significant for understanding inherent interconnections and influence within the network. The most common methods for representing social networks (node-link diagrams and adjacency matrices) are not optimal for understanding triangles. We propose extending the adjacency matrix form to 3D for better visualization of network triads. We design a 3D matrix reordering technique and implement an immersive interactive system to assist in visualizing and analyzing closed triads in social networks. The evaluations demonstrate that our method provides substantial added value over node-link diagrams in improving the efficiency and accuracy of manipulating and understanding the social network triads.
Recent research revealed that embedding a node-link diagram in a flat torus avoids edge crossings, improves aesthetic metrics, and has advantages in tasks such as path tracking and understanding network structures. Ho...
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ISBN:
(纸本)9798350393811;9798350393804
Recent research revealed that embedding a node-link diagram in a flat torus avoids edge crossings, improves aesthetic metrics, and has advantages in tasks such as path tracking and understanding network structures. However, the effectiveness of torus layouts using graphs and the influence of the cell size, the size of the torus space used during torus layouts on the drawing results have not been investigated. In this study, we clarified that the optimal cell size that minimizes the stress of drawing results differs depending on the graph through computational experiments using benchmark graph data. Moreover, we uncovered that in graphs with enabled torus layouts, the stress function depending on the cell size, is close to an unimodal function. We focused on this unimodal property and proposed an algorithm to determine whether a torus is valid from the drawing results and the optimal cell size using the golden-section search. Reportedly, the aesthetic metrics of graphs with optimal cell sizes outperformed empirically used cell sizes through computational experiments.
The cluster faithfulness metrics CQ measure how faithfully the ground truth clustering of a graph is represented as the geometric clustering in a drawing of the graph. Existing CQ metrics use k-means clustering, which...
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ISBN:
(纸本)9798350393811;9798350393804
The cluster faithfulness metrics CQ measure how faithfully the ground truth clustering of a graph is represented as the geometric clustering in a drawing of the graph. Existing CQ metrics use k-means clustering, which effectively compute a geometric clustering when the cluster sizes are even, resulting in accurate CQ metrics. However, k-means clustering tends to compute clusters of even sizes and thus often fails to compute an accurate geometric clustering when the cluster sizes are uneven, leading to inaccurate CQ metrics. In this paper, we present a new cluster faithfulness metric CQHAC, using HAC (Hierarchical Agglomerative Clustering). HAC can compute a more accurate geometric clustering for uneven cluster sizes than k-means clustering. Consequently, CQ-HAC can more accurately measure cluster faithfulness, regardless of whether the sizes of clusters are even or uneven. Moreover, we present two algorithms, Cluster-kmeans and Cluster-HAC, for optimizing cluster faithfulness of graphdrawings. Extensive experiments show that in practice, both algorithms always compute perfectly clusterfaithful drawings (i.e., CQ = 1) in our experiments using various graphs with both even and uneven cluster sizes, achieving significant improvement over existing graph layouts, including cluster-focused layouts.
Visualizing a graph directly via its adjacency matrix is a common and effective technique. Such matrix visualizations rely crucially on a good ordering of the vertices to highlight intrinsic patterns in the graph. Whe...
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ISBN:
(纸本)9798350393811;9798350393804
Visualizing a graph directly via its adjacency matrix is a common and effective technique. Such matrix visualizations rely crucially on a good ordering of the vertices to highlight intrinsic patterns in the graph. When analyzing collections of graphs, such as time varying sequences or connectivity information ranging over multiple specimens, the user currently needs to make the choice: either order each graph individually to optimize its ordering quality, or use a single, simultaneous ordering for all graphs in the collection, which necessarily reduces the ordering quality for the individual graphs. In this paper we explore the space of contextual orderings that lie between these two extremes. Intuitively, contextual orderings maintain a higher level of consistency than individual orderings and deliver a higher ordering quality than simultaneous orderings. To formally reason about contextual orderings we define a distance measure between orderings which is based on individual block moves (IBM). The IBM distance allows us to relate consistency within the context of the collection with ordering quality. Specifically, we define the consistency of an ordering as the IBM distance to the simultaneous ordering for the collection. Our experiments show that already at a small IBM distance to the simultaneous ordering we can find contextual orderings with significantly improved ordering quality. Furthermore, we can create orderings that are nearly as good as individual orderings, but exhibit considerably improved consistency. We hence believe that contextual orderings can enable a more fine-grained analysis of graph collections, by allowing the user to focus on individual graphs while maintaining a sense of the context they appear in.
Many data sets, crucial for today's applications, consist of enormous networks, containing millions or even billions of elements. Having the possibility of visualizing such networks is of paramount importance. We ...
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ISBN:
(纸本)9798350393811;9798350393804
Many data sets, crucial for today's applications, consist of enormous networks, containing millions or even billions of elements. Having the possibility of visualizing such networks is of paramount importance. We propose an algorithmic framework and a visual metaphor, dubbed Treebar Maps, to provide schematic representations of huge networks. Our goal is to convey the main features of the network's inner structure in a straightforward, two-dimensional, one-page drawing, that effectively captures the essential quantitative information about the network's main components. Experiments show that we are able to create such representations in a few hundreds of seconds. We demonstrate the metaphor's efficacy through visual examination of extensive graphs, highlighting how their diverse structures are instantly comprehensible via their representations.
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