Permuting web graphs

Since the first investigations on web graph compression, it has been clear that the ordering of the nodes of the graph has a fundamental influence on the compression rate (usually expressed as the number of bits per link). The authors of the LINK database, for instance, investigated three different approaches: an extrinsic ordering (URL ordering) and two intrinsic (or coordinate-free) orderings based on the rows of the adjacency matrix (lexicographic and Gray code); they concluded that URL ordering has many advantages in spite of a small penalty in compression. In this paper we approach this issue in a more systematic way, testing some old orderings and proposing some new ones. Our experiments are made in the WebGraph framework, and show that the compression technique and the structure of the graph can produce significantly different results. In particular, we show that for the transpose web graph URL ordering is significantly less effective, and that some new orderings combining host information and Gray/lexicographic orderings outperform all previous methods. In particular, in some large transposed graphs they yield the quite incredible compression rate of 1 bit per link.