A variety of lossless compression schemes has been proposed to reduce the storage requirements of web graphs. One successful approach is virtual-node compression, in which often-used patterns of links are replaced by links to virtual nodes, creating a compressed graph that succinctly represents the original. In this paper, we show that several important classes of web graph algorithms can be extended to run directly on virtual-node-compressed graphs, such that their running times depend on the size of the compressed graph rather than on that of the original. These include algorithms for link analysis, estimating the size of vertex neighborhoods, and a variety of algorithms based on matrix-vector products and random walks. Similar speedups have been obtained previously for classical graph algorithms such as shortest paths and maximum bipartite matching. We measure the performance of our modified algorithms on several publicly available web graph data sets, and demonstrate significant empirical speedups that nearly match the compression ratios.
"Speeding Up Algorithms on Compressed Web Graphs." Internet Math. 6 (3) 373 - 398, 2009.