• Documents
  • Authors
  • Tables
  • Log in
  • Sign up
  • MetaCart
  • DMCA
  • Donate

CiteSeerX logo

Advanced Search Include Citations
Advanced Search Include Citations

DMCA

Graph evolution: Densification and shrinking diameters (2007)

Cached

  • Download as a PDF

Download Links

  • [arxiv.org]
  • [arxiv.org]
  • [arxiv.org]
  • [www.cs.cmu.edu]
  • [www.cs.cmu.edu]
  • [cs.stanford.edu]
  • [www-2.cs.cmu.edu]
  • [compmath.files.wordpress.com]
  • [snap.stanford.edu]
  • [people.seas.harvard.edu]
  • [www.db.cs.cmu.edu]

  • Other Repositories/Bibliography

  • DBLP
  • Save to List
  • Add to Collection
  • Correct Errors
  • Monitor Changes
by Jure Leskovec , Jon Kleinberg , Christos Faloutsos
Venue:ACM TKDD
Citations:266 - 15 self
  • Summary
  • Citations
  • Active Bibliography
  • Co-citation
  • Clustered Documents
  • Version History

BibTeX

@ARTICLE{Leskovec07graphevolution:,
    author = {Jure Leskovec and Jon Kleinberg and Christos Faloutsos},
    title = {Graph evolution: Densification and shrinking diameters},
    journal = {ACM TKDD},
    year = {2007},
    pages = {2}
}

Share

Facebook Twitter Reddit Bibsonomy

OpenURL

 

Abstract

How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing super-linearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) or O(log(log n)). Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a “forest fire” spreading process, that has a simple, intuitive justification, requires very few parameters (like the “flammability ” of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. We also notice that the “forest fire” model exhibits a sharp transition between sparse graphs and graphs that are densifying. Graphs with decreasing distance between the nodes are generated around this transition point. Last, we analyze the connection between the temporal evolution of the degree distribution and densification of a graph. We find that the two are fundamentally related. We also observe that real networks exhibit this type of r

Keyphrases

graph evolution    static graph    network evolution    average distance    temporal evolution    many study    long period    surprising phenomenon    qualitative level    intuitive justification    out-degree distribution    full range    graph generation model    real graph    small-world phenomenon    degree distribution    new graph generator    conventional wisdom    small number    sharp transition    prior work    present study    forest fire    transition point    real graph evolve    single snapshot    sparse graph    normal growth pattern    real network    wide range    information network    large network    heavy tail    fire model    distance parameter   

Powered by: Apache Solr
  • About CiteSeerX
  • Submit and Index Documents
  • Privacy Policy
  • Help
  • Data
  • Source
  • Contact Us

Developed at and hosted by The College of Information Sciences and Technology

© 2007-2019 The Pennsylvania State University