Figure 1

Illustration of ranking by PageRank on a 6 × 6 grid. Rankings by degree and by PageRank fail in this simple example. Vertices on the inner two layers have the same degree, 4. But the difference of those vertices can be measured by KSD. The colors from dark blue to light blue represent changes of the rank from high to low. PageRank with the damping parameter 1 yields same ordering as ranking by degree. The plot is the ordering result by PageRank with the damping parameter ∈ (0, 1).