Abstract

The power law arises commonly in modeling the number of vertices of a given degree in large graphs. In estimating the degree of the power law, the typical approach is to truncate by eye the log-log plot, then fit a linear equation to the remaining log-transformed data. Here we formulate a hard-coded truncation rule to replace the visual truncation, justify it by showing that the truncation point goes to infinity and misses a vanishing fraction of the data with probability tending to one, and refine the subsequent regression with a weighting and a way to use the covariation between slope and intercept to optimize the slope estimate.

Original languageEnglish (US)
Pages (from-to)19-28
Number of pages10
JournalInternet Mathematics
Volume6
Issue number1
DOIs
StatePublished - Jan 1 2009

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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