Fast generation of sparse random kernel graphs

Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo

doi:10.1371/journal.pone.0135177

Fast generation of sparse random kernel graphs

Journal Article · Thu Sep 10 00:00:00 EDT 2015 · PLoS ONE

DOI:https://doi.org/10.1371/journal.pone.0135177· OSTI ID:1222471

Hagberg, Aric ^[1]; Lemons, Nathan ^[1]; Du, Wen -Bo ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Beihang Univ. (China)

The development of kernel-based 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 real-world networks are usually large, it is essential that the run-time 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 power-law degree distribution graphs with tunable assortativity.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1222471

Journal Information:: PLoS ONE, Journal Name: PLoS ONE Journal Issue: 9 Vol. 10; ISSN 1932-6203

Publisher:: Public Library of ScienceCopyright Statement

Country of Publication:: United States

Language:: English

References (30)

Simple Markov-chain algorithms for generating bipartite graphs and tournaments Kannan, Ravi; Tetali, Prasad; Vempala, Santosh Random Structures and Algorithms, Vol. 14, Issue 4 https://doi.org/10.1002/(sici)1098-2418(199907)14:4<293::aid-rsa1>3.0.co;2-g	journal	July 1999
Asymptotic equivalence and contiguity of some random graphs Janson, Svante Random Structures and Algorithms, Vol. 36, Issue 1 https://doi.org/10.1002/rsa.20297	journal	January 2010
Modeling and Simulation of Large Biological, Information and Socio-Technical Systems: An Interaction Based Approach Barrett, Chris; Eubank, Stephen; Marathe, Madhav Interactive Computation https://doi.org/10.1007/3-540-34874-3_14	book	January 2006
Are We There Yet? When to Stop a Markov Chain while Generating Random Graphs Ray, Jaideep; Pinar, Ali; Seshadhri, C. Lecture Notes in Computer Science https://doi.org/10.1007/978-3-642-30541-2_12	book	January 2012
A Sequential Algorithm for Generating Random Graphs Bayati, Mohsen; Kim, Jeong Han; Saberi, Amin Algorithmica, Vol. 58, Issue 4 https://doi.org/10.1007/s00453-009-9340-1	journal	July 2009
Resisting structural re-identification in anonymized social networks Hay, Michael; Miklau, Gerome; Jensen, David The VLDB Journal, Vol. 19, Issue 6 https://doi.org/10.1007/s00778-010-0210-x	journal	December 2010
The asymptotic number of labeled graphs with given degree sequences Bender, Edward A.; Canfield, E. Rodney Journal of Combinatorial Theory, Series A, Vol. 24, Issue 3 https://doi.org/10.1016/0097-3165(78)90059-6	journal	May 1978
A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs Bollobás, Béla European Journal of Combinatorics, Vol. 1, Issue 4 https://doi.org/10.1016/s0195-6698(80)80030-8	journal	December 1980
A Random Graph Model for Power Law Graphs Aiello, William; Chung, Fan; Lu, Linyuan Experimental Mathematics, Vol. 10, Issue 1 https://doi.org/10.1080/10586458.2001.10504428	journal	January 2001
A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees Blitzstein, Joseph; Diaconis, Persi Internet Mathematics, Vol. 6, Issue 4 https://doi.org/10.1080/15427951.2010.557277	journal	March 2011
Efficient generation of large random networks Batagelj, Vladimir; Brandes, Ulrik Physical Review E, Vol. 71, Issue 3 https://doi.org/10.1103/physreve.71.036113	journal	March 2005
A Scalable Generative Graph Model with Community Structure Kolda, Tamara G.; Pinar, Ali; Plantenga, Todd SIAM Journal on Scientific Computing, Vol. 36, Issue 5 https://doi.org/10.1137/130914218	journal	January 2014
Random Graphs Gilbert, E. N. The Annals of Mathematical Statistics, Vol. 30, Issue 4 https://doi.org/10.1214/aoms/1177706098	journal	December 1959
Sparse random graphs with clustering Bollobas, Bela; Janson, Svante; Riordan, Oliver arXiv https://doi.org/10.48550/arxiv.0807.2040	text	January 2008
The phase transition in inhomogeneous random graphs Bollobas, Bela; Janson, Svante; Riordan, Oliver arXiv https://doi.org/10.48550/arxiv.math/0504589	text	January 2005
Simple Markov-chain algorithms for generating bipartite graphs and tournaments Kannan, Ravi; Tetali, Prasad; Vempala, Santosh Random Structures and Algorithms, Vol. 14, Issue 4 https://doi.org/10.1002/(SICI)1098-2418(199907)14:4<293::AID-RSA1>3.0.CO;2-G	journal	July 1999
The phase transition in inhomogeneous random graphs Bollobás, Béla; Janson, Svante; Riordan, Oliver Random Structures and Algorithms, Vol. 31, Issue 1 https://doi.org/10.1002/rsa.20168	journal	January 2007
Sparse random graphs with clustering Bollobás, Béla; Janson, Svante; Riordan, Oliver Random Structures & Algorithms, Vol. 38, Issue 3 https://doi.org/10.1002/rsa.20322	journal	March 2011
Connected Components in Random Graphs with Given Expected Degree Sequences Chung, Fan; Lu, Linyuan Annals of Combinatorics, Vol. 6, Issue 2 https://doi.org/10.1007/PL00012580	journal	November 2002
A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs Bollobás, Béla European Journal of Combinatorics, Vol. 1, Issue 4 https://doi.org/10.1016/S0195-6698(80)80030-8	journal	December 1980
Modelling dynamical processes in complex socio-technical systems Vespignani, Alessandro Nature Physics, Vol. 8, Issue 1 https://doi.org/10.1038/nphys2160	journal	December 2011
Some features of the spread of epidemics and information on a random graph Durrett, Rick Proceedings of the National Academy of Sciences, Vol. 107, Issue 10 https://doi.org/10.1073/pnas.0914402107	journal	February 2010
Networks Newman, Mark https://doi.org/10.1093/acprof:oso/9780199206650.001.0001	book	March 2010
General formalism for inhomogeneous random graphs Söderberg, Bo Physical Review E, Vol. 66, Issue 6 https://doi.org/10.1103/PhysRevE.66.066121	journal	December 2002
Efficient generation of large random networks Batagelj, Vladimir; Brandes, Ulrik Physical Review E, Vol. 71, Issue 3 https://doi.org/10.1103/PhysRevE.71.036113	journal	March 2005
Community structure and scale-free collections of Erdős-Rényi graphs Seshadhri, C.; Kolda, Tamara G.; Pinar, Ali Physical Review E, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevE.85.056109	journal	May 2012
Uncovering disassortativity in large scale-free networks Litvak, Nelly; van der Hofstad, Remco Physical Review E, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRevE.87.022801	journal	February 2013
Assortative Mixing in Networks Newman, M. E. J. Physical Review Letters, Vol. 89, Issue 20 https://doi.org/10.1103/PhysRevLett.89.208701	journal	October 2002
Statistical mechanics of complex networks Albert, Réka; Barabási, Albert-László Reviews of Modern Physics, Vol. 74, Issue 1 https://doi.org/10.1103/RevModPhys.74.47	journal	January 2002
The Structure and Function of Complex Networks Newman, M. E. J. SIAM Review, Vol. 45, Issue 2 https://doi.org/10.1137/S003614450342480	journal	January 2003

Similar Records

Constructing and sampling graphs with a given joint degree distribution.

Conference · Wed Sep 01 00:00:00 EDT 2010 · OSTI ID:1030342

Coloring geographical threshold graphs

Conference · Mon Dec 31 23:00:00 EST 2007 · OSTI ID:956667

Evolution of a Modified Binomial Random Graph by Agglomeration

Journal Article · Wed Feb 14 23:00:00 EST 2018 · Journal of Statistical Physics · OSTI ID:22784013

Related Subjects

97 MATHEMATICS AND COMPUTING
algorithms
computing systems
graphs
integrals
kernel methods
mathematical models
network analysis
random variables

Fast generation of sparse random kernel graphs

Citation Formats

References (30)

Similar Records

Related Subjects