A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees
Random graphs with given degrees are a natural next step in complexity beyond the Erdős-Rényi model, yet the degree constraint greatly complicates simulation and estimation. We use an extension of a combinatorial characterization due to Erdős and Gallai to develop a sequential algorithm for generati...
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| Veröffentlicht in: | Internet mathematics Jg. 6; H. 4; S. 489 - 522 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Taylor & Francis Group
09.03.2011
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| ISSN: | 1542-7951, 1944-9488 |
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| Abstract | Random graphs with given degrees are a natural next step in complexity beyond the Erdős-Rényi model, yet the degree constraint greatly complicates simulation and estimation. We use an extension of a combinatorial characterization due to Erdős and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows for surprisingly efficient sequential importance sampling. The resulting probabilities are easily computed on the fly, allowing the user to reweight estimators appropriately, in contrast to some ad hoc approaches that generate graphs with the desired degrees but with completely unknown probabilities. Applications are given, including simulating an ecological network and estimating the number of graphs with a given degree sequence. |
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| AbstractList | Random graphs with given degrees are a natural next step in complexity beyond the Erdős-Rényi model, yet the degree constraint greatly complicates simulation and estimation. We use an extension of a combinatorial characterization due to Erdős and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows for surprisingly efficient sequential importance sampling. The resulting probabilities are easily computed on the fly, allowing the user to reweight estimators appropriately, in contrast to some ad hoc approaches that generate graphs with the desired degrees but with completely unknown probabilities. Applications are given, including simulating an ecological network and estimating the number of graphs with a given degree sequence. |
| Author | Diaconis, Persi Blitzstein, Joseph |
| Author_xml | – sequence: 1 givenname: Joseph surname: Blitzstein fullname: Blitzstein, Joseph organization: Department of Statistics , Harvard University – sequence: 2 givenname: Persi surname: Diaconis fullname: Diaconis, Persi organization: Departments of Mathematics and Statistics , Stanford University |
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| Cites_doi | 10.1007/978-1-4612-1023-8 10.1007/BF01275671 10.1515/9781400833993 10.1198/016214504000001303 10.1007/PL00012580 10.1007/978-1-4612-0801-3_3 10.1007/978-1-4757-3437-9_1 10.1017/S0963548399003867 10.1016/S0378-8733(98)00012-4 10.1017/CBO9780511721335.010 10.2307/2289017 10.1016/S0195-6698(80)80030-8 10.1007/978-1-4757-2553-7 10.1214/105051604000000693 10.1214/009053605000000822 10.2307/1943071 10.1016/0304-3975(90)90164-D 10.1137/1028156 10.1007/978-3-7091-9076-0_12 10.1111/j.1467-9531.2006.00176.x 10.1073/pnas.252631999 10.2307/2287037 10.1137/S003614450342480 10.1007/978-1-4757-4321-0 10.1007/s00453-009-9340-1 10.2307/2669533 10.1214/08-AAP558 10.1007/BF02294482 10.2307/2291224 10.2307/2669847 10.1198/106186007X209226 10.1126/science.298.5594.824 10.1016/S0195-6698(13)80042-X 10.1017/S0963548306007978 10.1038/30918 10.1214/aos/1030563990 10.1016/0097-3165(78)90059-6 10.1137/0110037 10.1093/oso/9780198534891.001.0001 10.1016/j.aim.2003.10.007 |
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| References | Erdös and Gallai 60 (CIT0025) 1960; 11 CIT0032 Liu 01 (CIT0041) 2001 Park and Newman 04 (CIT0052) 2004; 70 Bassetti and Diaconis 05 (CIT0006) 2006; 50 CIT0036 CIT0035 Rubinstein and Kroese 04 (CIT0055) 2004 CIT0038 King 04 (CIT0037) 2004; 70 R Core Team 05 (CIT0053) 2005 CIT0042 Hammersley and Handscomb 65 (CIT0030) 1965 Wormald 99 (CIT0067) 1999 Lehmann and Romano 05 (CIT0040) 2005 Fishman 66 (CIT0026) 1996 Macdonald 95 (CIT0043) 1995 CIT0003 CIT0047 CIT0002 CIT0046 Robins et al. 07 (CIT0054) 2007; 29 CIT0049 CIT0004 Jackson 08 (CIT0034) 2008 McKay and Wormald 90 (CIT0045) 1990; 11 CIT0007 Snijders 02 (CIT0059) 2002; 3 CIT0009 Mahadev and Peled 95 (CIT0044) 1995 Newman 01 (CIT0048) 2001; 64 CIT0051 CIT0011 Chatterjee et al. 11 (CIT0014) 2011 Ellson et al. 03 (CIT0024) 2003 Diaconis and Gangolli 95 (CIT0021) 1995 Tinhofer 79 (CIT0062) 1979; 13 CIT0058 CIT0057 CIT0016 CIT0015 CIT0018 CIT0017 CIT0019 CIT0061 CIT0060 CIT0065 CIT0020 CIT0022 Bollobás 80 (CIT0013) 1980; 1 Doucet et al. 01 (CIT0023) 2001 Lauritzen 88 (CIT0039) 1988 Tinhofer 90 (CIT0063) 1990; 7 Admiraal and Handcock 08 (CIT0001) 2008; 24 Havel 55 (CIT0031) 1955; 80 Beichl and Cloteaux 08 (CIT0008) 2008 Itzkovitz et al. 03 (CIT0033) 2003; 68 CIT0027 CIT0029 Goulden and Jackson 04 (CIT0028) 2004 |
| References_xml | – volume-title: Extremal Families and Systems of Sufficient Statistics, Lecture Notes in Statistics 49 year: 1988 ident: CIT0039 doi: 10.1007/978-1-4612-1023-8 – ident: CIT0046 doi: 10.1007/BF01275671 – volume-title: Social and Economic Networks year: 2008 ident: CIT0034 doi: 10.1515/9781400833993 – ident: CIT0016 doi: 10.1198/016214504000001303 – ident: CIT0019 doi: 10.1007/PL00012580 – start-page: 15 volume-title: In Discrete Probability and Algorithms (Minneapolis, MN, 1993) year: 1995 ident: CIT0021 doi: 10.1007/978-1-4612-0801-3_3 – volume-title: Monte Carlo Strategies in Scientific Computing, Springer Series in Statistics year: 2001 ident: CIT0041 – volume: 68 start-page: 8 year: 2003 ident: CIT0033 publication-title: Phys. Rev. E (3) – start-page: 3 volume-title: Sequential Monte Carlo Methods in Practice, Stat. Eng. Inf. Sci. year: 2001 ident: CIT0023 doi: 10.1007/978-1-4757-3437-9_1 – ident: CIT0060 doi: 10.1017/S0963548399003867 – volume-title: R: A Language and Environment for Statistical Computing year: 2005 ident: CIT0053 – volume: 80 start-page: 477 year: 1955 ident: CIT0031 publication-title: C˘asopis Pĕst. Mat. – ident: CIT0002 doi: 10.1016/S0378-8733(98)00012-4 – start-page: 239 volume-title: In Surveys in Combinatorics, 1999 (Canterbury) year: 1999 ident: CIT0067 doi: 10.1017/CBO9780511721335.010 – ident: CIT0027 doi: 10.2307/2289017 – volume: 1 start-page: 311 year: 1980 ident: CIT0013 publication-title: European J. Combin. doi: 10.1016/S0195-6698(80)80030-8 – volume-title: Monte Carlo: Concepts, Algorithms, and Applications, Springer Series in Operations Research year: 1996 ident: CIT0026 doi: 10.1007/978-1-4757-2553-7 – ident: CIT0003 doi: 10.1214/105051604000000693 – ident: CIT0017 doi: 10.1214/009053605000000822 – volume: 11 start-page: 264 year: 1960 ident: CIT0025 publication-title: Mat. Lapok – ident: CIT0004 doi: 10.2307/1943071 – start-page: 127 volume-title: Graph Drawing Software year: 2003 ident: CIT0024 – ident: CIT0035 doi: 10.1016/0304-3975(90)90164-D – ident: CIT0061 doi: 10.1137/1028156 – volume: 70 start-page: 3 year: 2004 ident: CIT0037 publication-title: Phys. Rev. E – volume: 7 start-page: 235 year: 1990 ident: CIT0063 publication-title: Computing Supplementum doi: 10.1007/978-3-7091-9076-0_12 – ident: CIT0057 doi: 10.1111/j.1467-9531.2006.00176.x – year: 2011 ident: CIT0014 publication-title: To appear in Annals of Applied Probability – ident: CIT0018 doi: 10.1073/pnas.252631999 – ident: CIT0032 doi: 10.2307/2287037 – volume: 3 start-page: 1 year: 2002 ident: CIT0059 publication-title: Journal of Social Structure – volume: 70 start-page: 13 year: 2004 ident: CIT0052 publication-title: Phys. Rev. E (3) – ident: CIT0049 doi: 10.1137/S003614450342480 – volume: 50 year: 2006 ident: CIT0006 publication-title: Illinois Journal of Mathematics – volume-title: The Cross-Entropy Method, Information Science and Statistics year: 2004 ident: CIT0055 doi: 10.1007/978-1-4757-4321-0 – volume: 29 start-page: 92 year: 2007 ident: CIT0054 publication-title: Social Networks – ident: CIT0007 doi: 10.1007/s00453-009-9340-1 – volume-title: Monte Carlo Methods year: 1965 ident: CIT0030 – start-page: 1020 year: 2008 ident: CIT0008 publication-title: In Proceedings of the 40th Conference on Winter Simulation, Winter Simulation Conference – ident: CIT0051 doi: 10.2307/2669533 – ident: CIT0011 doi: 10.1214/08-AAP558 – volume-title: Combinatorial Enumeration year: 2004 ident: CIT0028 – ident: CIT0058 doi: 10.1007/BF02294482 – ident: CIT0038 doi: 10.2307/2291224 – ident: CIT0042 doi: 10.2307/2669847 – volume: 64 year: 2001 ident: CIT0048 publication-title: Physical Review E – ident: CIT0015 doi: 10.1198/106186007X209226 – ident: CIT0047 doi: 10.1126/science.298.5594.824 – volume: 11 start-page: 565 year: 1990 ident: CIT0045 publication-title: European J. Combin. doi: 10.1016/S0195-6698(13)80042-X – ident: CIT0020 doi: 10.1017/S0963548306007978 – volume: 13 start-page: 265 year: 1979 ident: CIT0062 publication-title: Applied Computer Science Berichte Praktische Informatik – ident: CIT0065 doi: 10.1038/30918 – ident: CIT0022 doi: 10.1214/aos/1030563990 – volume-title: Testing Statistical Hypotheses, Springer Texts in Statistics year: 2005 ident: CIT0040 – volume-title: Threshold Graphs and Related Topics, Annals of Discrete Mathematics 56 year: 1995 ident: CIT0044 – ident: CIT0009 doi: 10.1016/0097-3165(78)90059-6 – ident: CIT0029 doi: 10.1137/0110037 – volume-title: Symmetric Functions and Hall Polynomials year: 1995 ident: CIT0043 doi: 10.1093/oso/9780198534891.001.0001 – ident: CIT0036 doi: 10.1016/j.aim.2003.10.007 – volume: 24 start-page: 1 year: 2008 ident: CIT0001 publication-title: Journal of Statistical Software |
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| Title | A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees |
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