Cited by 967Complexity and Algorithms in GraphsComplex Network Analysis TechniquesGraph Theory and Algorithms

Local Graph Partitioning using PageRank Vectors

Andersen, Reid, Chung, Fan, Lang, Kevin·2006·2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)

Abstract

A local graph partitioning algorithm finds a cut near a specified starting vertex, with a running time that depends largely on the size of the small side of the cut, rather than the size of the input graph. In this paper, we present a local partitioning algorithm using a variation of PageRank with a specified starting distribution. We derive a mixing result for PageRank vectors similar to that for random walks, and show that the ordering of the vertices produced by a PageRank vector reveals a cut with small conductance. In particular, we show that for any set C with conductance Phi and volume k, a PageRank vector with a certain starting distribution can be used to produce a set with conductance (O(radic(Phi log k)). We present an improved algorithm for computing approximate PageRank vectors, which allows us to find such a set in time proportional to its size. In particular, we can find a cut with conductance at most oslash, whose small side has volume at least 2bin time O(2 log m/(2blog2m/oslash2) where m is the number of edges in the graph. By combining small sets found by this local partitioning algorithm, we obtain a cut with conductance oslash and approximately optimal balance in time O(m log4m/oslash)

Integrity signals

Registry

Crossref · 10.1109/focs.2006.44

Cites

22 of 22 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Cites

Flagged first, then by citations

1 of the 23 references couldn’t be matched to a known paper.

Cited by

Sorted by citations

Authors
Andersen, R., Chung, F., & Lang, K.
Affiliations
  • University of California San Diego (US)
  • Yahoo (United States) (US)
Venue
2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
Publisher
IEEE
Published
2006
Pages
475-486
ISSN
0272-5428 (ISSN-L)
OpenAlex
W2086254934
Cited by
967
References
23
Citations by year
2026: 20 · 2025: 40 · 2024: 46 · 2023: 57 · 2022: 55 · 2021: 84 · 2020: 71 · 2019: 72 · 2018: 63 · 2017: 61 · 2016: 69 · 2015: 65 · 2014: 52 · 2013: 55 · 2012: 50
FWCI
13.60
Type
conference paper
Language
en
Open access
closed
Locations
Annual Symposium on Foundations of Computer Science (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Graph Theory and Algorithms
Keywords
graph cuts, conductance, random walks

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review