Fast generation of sparse random kernel graphs
The development of kernelbased inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As realworld networks are usually large, it is essential that the runtime of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most ο(n(logn)²). As an example, we show how to generate samples of powerlaw degree distribution graphs with tunable assortativity.
 Authors:

^{[1]};
^{[1]};
^{[2]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Beihang Univ. (China)
 Publication Date:
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 PLoS ONE
 Additional Journal Information:
 Journal Volume: 10; Journal Issue: 9; Journal ID: ISSN 19326203
 Publisher:
 Public Library of Science
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 graphs; algorithms; kernel methods; random variables; integrals; computing systems; mathematical models; network analysis
 OSTI Identifier:
 1222471
Hagberg, Aric, Lemons, Nathan, and Du, Wen Bo. Fast generation of sparse random kernel graphs. United States: N. p.,
Web. doi:10.1371/journal.pone.0135177.
Hagberg, Aric, Lemons, Nathan, & Du, Wen Bo. Fast generation of sparse random kernel graphs. United States. doi:10.1371/journal.pone.0135177.
Hagberg, Aric, Lemons, Nathan, and Du, Wen Bo. 2015.
"Fast generation of sparse random kernel graphs". United States.
doi:10.1371/journal.pone.0135177. https://www.osti.gov/servlets/purl/1222471.
@article{osti_1222471,
title = {Fast generation of sparse random kernel graphs},
author = {Hagberg, Aric and Lemons, Nathan and Du, Wen Bo},
abstractNote = {The development of kernelbased inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As realworld networks are usually large, it is essential that the runtime of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most ο(n(logn)²). As an example, we show how to generate samples of powerlaw degree distribution graphs with tunable assortativity.},
doi = {10.1371/journal.pone.0135177},
journal = {PLoS ONE},
number = 9,
volume = 10,
place = {United States},
year = {2015},
month = {9}
}