Graph sampling methods have been used to reduce the size and complexity of big complex networks for graph mining and visualization. However, existing graph sampling methods often fail to preserve the connectivity and important structures of the original graph. This paper introduces a new divide and conquer approach to spectral graph sampling based on graph connectivity, called the BC Tree (i.e., decomposition of a connected graph into biconnected components) and spectral sparsification. Specifically, we present two methods, spectral vertex sampling $$BC\_SV$$ B C _ S V and spectral edge sampling $$BC\_SS$$ B C _ S S by computing effective resistance values of vertices and edges for each connected component. Furthermore, we present $$DBC\_SS$$ D B C _ S S and $$DBC\_GD$$ D B C _ G D , graph connectivity-based distributed algorithms for spectral sparsification and graph drawing respectively, aiming to further improve the runtime efficiency of spectral sparsification and graph drawing by integrating connectivity-based graph decomposition and distributed computing. Experimental results demonstrate that $$BC\_SV$$ B C _ S V and $$BC\_SS$$ B C _ S S are significantly faster than previous spectral graph sampling methods while preserving the same sampling quality. $$DBC\_SS$$ D B C _ S S and $$DBC\_GD$$ D B C _ G D obtain further significant runtime improvement over sequential approaches, and $$DBC\_GD$$ D B C _ G D further achieves significant improvements in quality metrics over sequential graph drawing layouts.
In this paper, we present a new framework for sublinear time force computation for visualization of big complex graphs. Our algorithm is based on the sampling of vertices for computing repulsion forces and edge sparsification for attraction force computation. More specifically, for vertex sampling, we present three types of sampling algorithms, including random sampling, geometric sampling, and combinatorial sampling, to reduce the repulsion force computation to sublinear in the number of vertices. We utilize a spectral sparsification approach to reduce the number of attraction force computations to sublinear in the number of edges for dense graphs. We also present a smart initialization method based on radial tree drawing of the BFS spanning tree rooted at the center. Experiments show that our new sublinear time force computation algorithms run quite fast, while producing good visualization of large and complex networks, with significant improvements in quality metrics such as shape‐based and edge crossing metrics.
Recent methods for visualizing graphs have used a map metaphor: vertices are represented as regions in the plane, and proximity between regions represents edges between vertices.In many real world applications, the data changes over time, resulting in a dynamic map. This paper introduces new methods for representing dynamic graphs with map animation. More specifically, we present three different animation methods: MDSV (Multidimensional scaling -Voronoi), TV (Tutte -Voronoi) and TD (Tutte -dual). These methods support operations such as addition and deletion of vertices and edges. Each of our methods uses a kind of matrix interpolation.
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