基于超图结构的科研合作网络演化模型

胡枫; 赵海兴; 何佳倍; 李发旭; 李淑玲; 张子柯

doi:10.7498/aps.62.198901

摘要

基于科研论文作者的合作方式, 用超图理论构建了一个科研合作超网络演化模型. 利用平均场理论分析了作者发表论文的演化规律, 发现作者的超度 (即发表论文数) 分布符合幂律分布. 进一步理论分析得到分布的幂指数γ与合作领域作者增长速度相关. γ越大, 新作者增长速度越快, 且存在关系: γ=1+L/M (L/M为作者增长率). 并通过对《物理学报》与《中国科学》2003–2012年期间作者发表论文进行了数据分析, 实证结果与理论分析及模拟结果能很好地符合. 本文对科研合作网络的理论和实证研究有一定的借鉴意义.

关键词:

Abstract

In this paper, by considering the collaborative scientific behaviors, a model for evolving hyper-network is proposed based on the hypergraph theory. We study analytically the dynamics of authors’ hyper-degree using mean-field approach. Results of both theoretical and numerical studies indicate that such a hyper-degree distribution follows a power-law decay, with the exponent γ=1+L/M, where L/M suggests the author growth rate of an evolving scientific network. In addition, empirical studies on ten-year journal data of Science China and Acta Physica Sinica from 2003 to 2012, shows that the present model can find good agreement with the empirical data. The proposed model may shed some light on the in-depth understanding of the structure and scientific collaboration networks.

Keywords:

作者及机构信息

1.
陕西师范大学计算机科学学院, 西安 710062;

2.
青海师范大学计算机学院, 西宁 810008;

3.
电子科技大学互联网科学中心, 成都 611731;

4.
杭州师范大学信息经济研究所, 杭州 310036

基金项目: 科技部973前期专项资助项目(批准号:2010CB334708);教育部长江学者与创新团队支持计划(批准号:IRT1068);国家自然科学基金地区科学基金(批准号:60863006,61164005);国家自然科学基金青年科学基金(批准号:11105024,11205040,1147015);青海省自然科学基金(批准号:2012-Z-943)和杭州师范大学科研启动基金及"攀登工程"计划资助的课题.

Authors and contacts

1.
School of Computer Science, Shaanxi Normal University, Xi’an 710062, China;

2.
School of Computer, Qinghai Normal University, Xining 810008, China;

3.
Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China;

4.
Institute of Information Economy, Hangzhou Normal University, Hangzhou 310036, China

Funds: Project supported by the National Basic Research Program of China (No. 2010CB334708), the Program for Changjiang Scholars and Innovative Research Team in Universities (No. IRT1068), the Fund for Less Developed Regions of the National Natural Science Foundation of China (Grant Nos. 60863006, 61164005), the Yong Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11105024, 11205040, 1147015), the Nature Science Foundation from Qinghai Province (No. 2012-Z-943), and the start-up research funding and Pandeng Project of Hangzhou Normal University.

参考文献

[1]	Erdös P, Rényi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[2]	Watts D, Strogates S H 1998 Nature 393 440
[3]	Barabási A L, Albert R 1999 Science 286 509
[4]	Davis G F, Greve H R 1997 Amer. J. Sociol. 103 1
[5]	Ramasco J J, Dorogovtsev S N, Pastor-Satorras R 2004 Phys. Rev. E 64 016131
[6]	Newman M E J 2001 Proc. Natl. Acad. Sci. U.S.A. 98 404
[7]	He Y, Zhang P P, Xu T, Jiang Y M, He D R 2004 Acta Phys. Sin. 53 1710 (in Chinese) [何阅, 张培培, 许田, 姜玉梅,何大韧 2004 物理学报 53 1710]
[8]	Liljeros F, Edling C R, Amaral L A N, Stanley H E, Aberg Y 2001 Nature 411 907
[9]	Newman M E J 2001 Phys. Rev. E 64 016131
[10]	Newman M E J 2001 Phys. Rev. E 64 016132
[11]	Barabási A L, Jeong H, Néda Z, Ravasz E, Schubet A, Vicsek T 2001 Physica A 311 590
[12]	Zhou T, Jin Y D, Wang B H, He D R, Zhang P P, He Y, Su B B, Chen K, Zhang Z Z 2007 Int. J. Mod. Phys. C 18 297
[13]	L L, Medo M, Yeung C H, Zhang Y C, Zhang Z K, Zhou T 2012 Phys. Rep. 519 1
[14]	Berge C 1973 Graphs and Hypergraphs (vol. 6) (New York: Elsevier) p389
[15]	Berge C 1989 Hypergraphs: Combinatorics of Finite Sets (Vol. 45) (Amsterdam: North-Holland Holl) p3
[16]	Estrada E, Juan A J, Rodríguez V 2006 Physica A 364 581
[17]	Ghoshal G, Zlatić, Caldarelli G, Newman M E J 2009 Phys. Rev. E 79 066118
[18]	Zlatić V, Ghoshal G, Caldarelli G 2009 Phys. Rev. E 80 036118
[19]	Zhang Z K, Liu C 2010 J. Stat. Mech. P10005
[20]	Wang J W, Rong L L, Deng Q H, Zhang J Y 2010 Eur. Phys. J. B 77 493
[21]	Hu F, Zhao H X, Ma X J 2013 Sci. Sin. Phys. Mech Astron. 43 16 (in Chinese) [胡枫, 赵海兴, 马秀娟 2013 中国科学: 物理学力学天文学 43 16]
[22]	Shi D H 2011 Theory of network Degree Distributions (Vol. 1) (Beijing: Higher Education Press) p60 (in Chinese) [史定华 2011 网络度分布理论 (第1版) (北京: 高等教育出版社) 第60页]

施引文献

[1]	Erdös P, Rényi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[2]	Watts D, Strogates S H 1998 Nature 393 440
[3]	Barabási A L, Albert R 1999 Science 286 509
[4]	Davis G F, Greve H R 1997 Amer. J. Sociol. 103 1
[5]	Ramasco J J, Dorogovtsev S N, Pastor-Satorras R 2004 Phys. Rev. E 64 016131
[6]	Newman M E J 2001 Proc. Natl. Acad. Sci. U.S.A. 98 404
[7]	He Y, Zhang P P, Xu T, Jiang Y M, He D R 2004 Acta Phys. Sin. 53 1710 (in Chinese) [何阅, 张培培, 许田, 姜玉梅,何大韧 2004 物理学报 53 1710]
[8]	Liljeros F, Edling C R, Amaral L A N, Stanley H E, Aberg Y 2001 Nature 411 907
[9]	Newman M E J 2001 Phys. Rev. E 64 016131
[10]	Newman M E J 2001 Phys. Rev. E 64 016132
[11]	Barabási A L, Jeong H, Néda Z, Ravasz E, Schubet A, Vicsek T 2001 Physica A 311 590
[12]	Zhou T, Jin Y D, Wang B H, He D R, Zhang P P, He Y, Su B B, Chen K, Zhang Z Z 2007 Int. J. Mod. Phys. C 18 297
[13]	L L, Medo M, Yeung C H, Zhang Y C, Zhang Z K, Zhou T 2012 Phys. Rep. 519 1
[14]	Berge C 1973 Graphs and Hypergraphs (vol. 6) (New York: Elsevier) p389
[15]	Berge C 1989 Hypergraphs: Combinatorics of Finite Sets (Vol. 45) (Amsterdam: North-Holland Holl) p3
[16]	Estrada E, Juan A J, Rodríguez V 2006 Physica A 364 581
[17]	Ghoshal G, Zlatić, Caldarelli G, Newman M E J 2009 Phys. Rev. E 79 066118
[18]	Zlatić V, Ghoshal G, Caldarelli G 2009 Phys. Rev. E 80 036118
[19]	Zhang Z K, Liu C 2010 J. Stat. Mech. P10005
[20]	Wang J W, Rong L L, Deng Q H, Zhang J Y 2010 Eur. Phys. J. B 77 493
[21]	Hu F, Zhao H X, Ma X J 2013 Sci. Sin. Phys. Mech Astron. 43 16 (in Chinese) [胡枫, 赵海兴, 马秀娟 2013 中国科学: 物理学力学天文学 43 16]
[22]	Shi D H 2011 Theory of network Degree Distributions (Vol. 1) (Beijing: Higher Education Press) p60 (in Chinese) [史定华 2011 网络度分布理论 (第1版) (北京: 高等教育出版社) 第60页]

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