Recent work for visualizing big graphs uses a proxy graph approach: the original graph is replaced by a proxy graph, which is much smaller than the original graph. The challenge for the proxy graph approach is to ensure that the proxy graph is a good representation of the original graph. However, previous work to compute proxy graphs using graph sampling techniques often fails to preserve connectivity and important global skeletal structure in the original graph.
This paper introduces two new families of proxy graph methods BCP-W and BCP-E, tightly integrating graph sampling methods with the BC (Block Cut-vertex) tree, which represents the decomposition of a graph into biconnected components. Experimental results using graph sampling quality metrics show that our new BC tree-based proxy graph methods produce significantly better results than existing sampling-based proxy graph methods: 25% improvement by BCP-W and 15% by BCP-E on average.
We also present DBCP, a BC tree-based proxy graph method for distributed environment. Experiments on the Amazon Cloud EC2 demonstrate that DBCP is scalable for big graph data sets; runtime speed-up of 77% for distributed 5-server on average.
Visual comparison using a graph layout method and the proxy quality metrics confirm that our new BC tree-based proxy graph methods are significantly better than existing sampling-based proxy graph method. Our main results lead to guidelines for computing sampling-based proxy graphs for visualization of big graphs.