Random Walks on Directed Networks: the Case of PageRank
Santo Fortunato, Alessandro Flammini
Abstract
PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability of being visited. We give some exact results on the distribution of PageRank in the cases in which the damping factor q approaches the two limit values 0 and 1. When q -> 0 and for several classes of graphs the distribution is a power law with exponent 2, regardless of the in-degree distribution. When q -> 1 it can always be derived from the in-degree distribution of the underlying graph, if the out-degree is the same for all nodes.
Create a lesson
Related papers
Distinct routes to phase transitions in spatial activation systems
Jialu Zhang, Guanyu Zhang, Leyang Xue et al.
District-Level Food Environment Indicators and Social Vulnerability in São Paulo
Pedro Lemes Sixel Lobo, Eric Tokuda, Kuruvilla Joseph Abraham et al.
Prompt Sensitivity of Generative Agents: Evidence from an Epidemic Model
Ross Williams, Niyousha Hosseinichimeh
Giant strongly biconnected components of directed networks: a generating function approach
Minsoo Yang, Reinhard Laubenbacher, Byungjoon Min
(k,n)-core percolation on hypergraphs with anchor nodes
Hoseung Jang, Byungjoon Min, Ginestra Bianconi
The complex relationship between anti-immigrant sentiment and exposure in the Netherlands
Benedikt Meylahn, Tommaso Giommoni, Mike Lees et al.