Directed PageRank
Directed PageRank (Link-Based Authority Ranking on Directed Graphs) · Also known as: PageRank, PR, Google PageRank, directed link analysis
Directed PageRank is a link-based authority scoring algorithm that assigns importance scores to nodes in a directed graph by iteratively redistributing rank through outgoing edges. Introduced by Brin and Page in 1998 as the backbone of Google Search, it measures not just how many in-links a node has but how authoritative the nodes pointing to it are.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
+3 more
When to use it
Use Directed PageRank when you need to rank nodes in a directed network by global authority rather than local connectivity. It is appropriate for citation networks (finding influential papers), web-link graphs, social networks with asymmetric follow/endorse relations, and any setting where the direction of influence matters and recursive prestige is theoretically meaningful. Avoid it when the network is undirected or when edge direction has no interpretable meaning, in which case eigenvector centrality is more appropriate. Also avoid it for very sparse directed graphs (few in-links) where scores collapse to noise, or when only local structural properties such as direct connections are of interest.
Strengths & limitations
- Captures global, recursive authority: a node's score reflects the quality, not just the quantity, of its in-links.
- Robust to sparse or heterogeneous connectivity through the teleportation term, which prevents rank sinks.
- Scales efficiently to very large graphs via sparse power iteration.
- Widely validated across domains: web, citation, biological, and social networks.
- Interpretable as a random-surfer stationary distribution, grounding results in a probabilistic model.
- Sensitive to the choice of damping factor d; the canonical 0.85 may not suit all network types.
- Ignores edge weights by default; weighted variants require additional normalisation steps.
- Convergence speed depends on the spectral gap of the transition matrix; some graphs converge slowly.
- Does not distinguish between different types or meanings of directed edges without domain-specific pre-processing.
Frequently asked
What is the damping factor and how should I choose it?
The damping factor d (default 0.85) is the probability that a random surfer follows an outgoing link rather than teleporting. Higher values give more weight to link structure; lower values spread scores more uniformly. Sensitivity analysis across d in [0.75, 0.95] is recommended for non-web networks.
How is Directed PageRank different from eigenvector centrality?
Eigenvector centrality is the principal eigenvector of the adjacency matrix and works naturally on undirected graphs. Directed PageRank adds a teleportation term, handles dangling nodes, and explicitly incorporates link direction, making it better suited to asymmetric directed networks.
Does Directed PageRank handle weighted edges?
The standard formulation uses unweighted edges. Weighted PageRank exists as an extension where M_{ij} is proportional to the weight of edge (j,i) divided by the total outgoing weight of j, preserving the column-stochastic property.
How many iterations does convergence typically require?
For most large sparse networks with d = 0.85, fewer than 100 power iterations achieve tolerance below 1e-6. Convergence is faster when the graph has a large spectral gap; near-bipartite or near-reducible graphs may require more iterations.
Can I use PageRank on an undirected network?
You can replace each undirected edge with two directed edges and apply the algorithm, but the result will equal eigenvector centrality on the symmetric graph. Use eigenvector centrality directly for undirected networks to avoid unnecessary complexity.
Sources
- Brin, S. & Page, L. (1998). The anatomy of a large-scale hypertextual Web search engine. Proceedings of the 7th International Conference on World Wide Web (WWW7), 107–117. Elsevier. link ↗
- Langville, A. N. & Meyer, C. D. (2006). Google's PageRank and Beyond: The Science of Search Engine Rankings. Princeton University Press. ISBN: 978-0-691-12202-1
How to cite this page
ScholarGate. (2026, June 3). Directed PageRank (Link-Based Authority Ranking on Directed Graphs). ScholarGate. https://scholargate.app/en/network-analysis/directed-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.
- Betweenness CentralityNetwork analysis↔ compare
- Degree CentralityNetwork analysis↔ compare
- Directed Community DetectionNetwork analysis↔ compare
- Directed Social Network AnalysisNetwork analysis↔ compare
- Eigenvector CentralityNetwork analysis↔ compare