Navigating Low-Dimensional and Hierarchical Population Networks

  • Ravi Kumar
  • David Liben-Nowell
  • Andrew Tomkins
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


Social networks are navigable small worlds, in which two arbitrary people are likely connected by a short path of intermediate friends that can be found by a “decentralized” routing algorithm using only local information. We develop a model of social networks based on an arbitrary metric space of points, with population density varying across the points. We consider rank-based friendships, where the probability that person u befriends person v is inversely proportional to the number of people who are closer to u than v is. Our main result is that greedy routing can find a short path (of expected polylogarithmic length) from an arbitrary source to a randomly chosen target, independent of the population densities, as long as the doubling dimension of the metric space of locations is low. We also show that greedy routing finds short paths with good probability in tree-based metrics with varying population distributions.


Social Network Short Path Target Person Doubling Dimension Recursive Social Structure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ravi Kumar
    • 1
  • David Liben-Nowell
    • 2
  • Andrew Tomkins
    • 1
  1. 1.Yahoo! ResearchSunnyvaleUSA
  2. 2.Department of Computer ScienceCarleton CollegeNorthfieldUSA

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