PageRank Centrality
Also known as: Google PageRank, Random Surfer Model, Link-Based Ranking, PageRank Merkeziliği
PageRank is a link-based centrality algorithm that assigns an importance score to each node in a directed graph by measuring how many high-quality nodes point to it. Introduced by Larry Page, Sergey Brin, Rajeev Motwani, and Terry Winograd at Stanford University in 1999, it became the mathematical foundation of the Google search engine and remains one of the most influential algorithms in network science and information retrieval.
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When to use it
PageRank is appropriate when you need to rank nodes in a directed graph by global structural importance, especially when edge direction encodes endorsement or influence (hyperlinks, citations, social follows). It assumes the graph can be modeled as a Markov chain and requires a connected or strongly connected component for clean convergence. It is less suitable for undirected networks where HITS or betweenness centrality may be preferred, and it can be sensitive to link spam or artificially inflated in-degree.
Strengths & limitations
- Principled probabilistic foundation via the random-surfer Markov chain model
- Scales to very large graphs through sparse matrix-vector products and power iteration
- Captures global graph topology, rewarding nodes endorsed by other high-scoring nodes
- Widely validated across web, citation, biological, and social network domains
- Requires a directed graph; application to undirected networks needs convention choices
- Convergence speed depends on the spectral gap of the transition matrix and can be slow for poorly connected graphs
- Sensitive to the choice of damping factor d; different values can substantially alter rankings
- Vulnerable to link-farm manipulation and artificially constructed in-links
Frequently asked
What does the damping factor d represent and how should it be chosen?
The damping factor d (typically 0.85) is the probability that the random surfer follows a link rather than teleporting to a random node. Values close to 1 make the algorithm more sensitive to graph structure but slower to converge and more prone to rank sinks; values close to 0 approach uniform ranking. The value 0.85 was empirically validated by Page and Brin for the web graph and is the standard default.
How does PageRank differ from degree centrality?
Degree centrality counts only the direct number of incoming links to a node, treating all sources equally. PageRank weights each incoming link by the score of the linking node, so an endorsement from a highly ranked node contributes more than one from a low-ranked node. This recursive definition captures global graph structure rather than just local connectivity.
Can PageRank be applied to undirected graphs?
Yes, but with caveats. An undirected graph must be converted to a directed representation by replacing each undirected edge with two directed edges. The resulting PageRank scores then equal a function of node degree, reducing the algorithm to a weighted degree centrality. For undirected networks, alternative centrality measures such as eigenvector centrality or betweenness centrality are often more informative.
Sources
- Page, L., Brin, S., Motwani, R., & Winograd, T. (1999). The PageRank citation ranking: Bringing order to the web. Stanford InfoLab Technical Report. link ↗
How to cite this page
ScholarGate. (2026, June 2). PageRank Centrality. ScholarGate. https://scholargate.app/en/network-analysis/pagerank
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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