Adaptive Damping Factor Selection for Optimal PageRank Convergence
Faculty Mentor Information
Jared Cantrell, Idaho State University
Presentation Date
7-16-2026
Abstract
The PageRank algorithm has used a fixed damping factor of 0.85 since its introduction by Brin and Page in 1998, despite this value having no theoretical justification. We show that the optimal damping factor depends on the spectral properties of the graph being ranked and can be computed in closed form. Using this optimal static value reduces Power Iteration computation by approximately 35 percent on synthetic graphs. We further investigate whether the damping factor can be adapted online as a graph evolves. We prove a negative result: on persistently reducible streaming graphs, which include most real-world networks, the natural spectral signals are algebraically constant and cannot drive adaptation. We validate this on a 1.14 million node Wikipedia interaction network. We then propose the spectral gap of the largest strongly connected component as an alternative signal and demonstrate that it succeeds where the natural signals fail, achieving a 70.4 percent iteration reduction with 91.1 percent ranking fidelity on a real messaging network.
Adaptive Damping Factor Selection for Optimal PageRank Convergence
The PageRank algorithm has used a fixed damping factor of 0.85 since its introduction by Brin and Page in 1998, despite this value having no theoretical justification. We show that the optimal damping factor depends on the spectral properties of the graph being ranked and can be computed in closed form. Using this optimal static value reduces Power Iteration computation by approximately 35 percent on synthetic graphs. We further investigate whether the damping factor can be adapted online as a graph evolves. We prove a negative result: on persistently reducible streaming graphs, which include most real-world networks, the natural spectral signals are algebraically constant and cannot drive adaptation. We validate this on a 1.14 million node Wikipedia interaction network. We then propose the spectral gap of the largest strongly connected component as an alternative signal and demonstrate that it succeeds where the natural signals fail, achieving a 70.4 percent iteration reduction with 91.1 percent ranking fidelity on a real messaging network.