A Collaboration Network Model with Multiple Evolving Factors
Xiu-Lian Xu1** , Chun-Ping Liu2 , Da-Ren He1
1 College of Physics Science and Technology, Yangzhou University, Yangzhou 2250022 College of Mathematical Science, Yangzhou University, Yangzhou 225002
Abstract ：To describe the empirical data of collaboration networks, several evolving mechanisms have been proposed, which usually introduce different dynamics factors controlling the network growth. These models can reasonably reproduce the empirical degree distributions for a number of well-studied real-world collaboration networks. On the basis of the previous studies, in this work we propose a collaboration network model in which the network growth is simultaneously controlled by three factors, including partial preferential attachment, partial random attachment and network growth speed. By using a rate equation method, we obtain an analytical formula for the act degree distribution. We discuss the dependence of the act degree distribution on these different dynamics factors. By fitting to the empirical data of two typical collaboration networks, we can extract the respective contributions of these dynamics factors to the evolution of each networks.
收稿日期: 2016-01-24
出版日期: 2016-04-29
:
89.75.Hc
(Networks and genealogical trees)
89.75.Fb
(Structures and organization in complex systems)
89.40.-a
(Transportation)
[1] Pastor-Satorras R and Vespignani A 2004 Evolution and Structure of the Internet: A Statistical Physics Approach (Cambridge: Cambridge University Press) [2] Faloutsos M et al 1999 Comput. Commun. Rev. 29 251 [3] Goswami B et al 2015 Sci. Rep. 5 18183 [4] Albert R et al 1999 Nature 401 130 [5] Schwartz A et al 2016 Med. Teach. 38 64 [6] Wagner A 2001 Mol. Biol. E 18 1283 [7] Li W F et al 2011 Proc. Natl. Acad. Sci. USA 108 3504 [8] Podani J et al 2001 Nat. Genet. 29 54 [9] Stelling J et al 2002 Nature 420 190 [10] Jeong H et al 2001 Nature 411 41 [11] Solé R V et al 2002 Adv. Complex Syst. 5 43 [12] Vazquez A et al 2003 Nat. Biotechnol. 21 697 [13] Wachs-Lopes G A and Rodrigues P S 2016 Expert Syst. Appl. 45 8 [14] Wasserman S and Faust K 1994 Social Network Analysis (Cambridge: Cambridge University Press) [15] Yang J and Leskovec J 2015 Knowled Ge Inf. Syst. 42 181 [16] Newman M E J 2003 SIAM Rev. 45 167 [17] Opsahl T 2013 Soc. Networks 35 159 [18] Albert R and Barabási A L 2000 Phys. Rev. Lett. 85 5234 [19] Watts D J and Strogatz S H 1998 Nature 393 440 [20] Newman M E J et al 2002 Proc. Natl. Acad. Sci. USA 99 2566 [21] Ramasco J J, Dorogovtsev S N and Pastor-Satorras R 2004 Phys. Rev. E 70 036106 [22] Abbasi1A and Altmann J 2011 Proceedings of the 44th Hawaii International Conference on System Sciences [23] Barabási A L, Jeong H, Ravasz R, Neda Z, Vicsek T and Schubert A 2002 Physica A 311 590 [24] Balland P A 2012 Regional Studies 46 741 [25] Wang J R, Wang J P, He Z and Xu H T 2016 Commun. Nonlinear Sci. Numer. Simul.on 31 47 [26] Chang H, Xu X L, Hu C K, Fu C H, Feng A X and He D R 2014 Physica A 416 378 [27] Zhang P P, Chen K, HeY, Zhou T, Su B B, Jin Y D, Chang H, Zhou Y P, Sun L C, Wang B H and He D R 2006 Physica A 360 599 [28] Chang H, Su B B, Zhou Y P and He D R 2007 Physica A 383 687 [29] Yan X Y and Wang M S 2010 Acta Phys. Sin. 59 851 (in Chinese) [30] Xu X L, Qu Y Q, Guan S, Jiang Y M and He D R 2011 Europhys. Lett. 93 68002 [31] Xu X L, Fu C H, Chang H and He D R 2011 Physica A 390 3719 [32] Zhou T, Wang B H, Jin Y D, He D R, Zhang P P, He Y, Su B B, Chen K, Zhang Z Z and Liu Z H 2007 Int. J. Mod. Phys. C 18 297 [33] Krapivsky P L, Redner S and Leyvraz F 2000 Phys. Rev. Lett. 85 4629 [34] Liu Z H, Lai Y C L, Ye N and Dasgupta P 2002 Phys. Lett. A 303 337 [35] Zhao Q G, Kong X X and Hou Z T 2009 Pramana J. Phys. 73 955 [36] Feng A X, Fu C H, Xu X L, Zhou Y P, Chang H, Wang J, He D R and Feng G L 2012 Physica A 391 2454
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
.
[11]
.
[12]
.
[13]
.
[14]
.
[15]
.
2016, Vol. 33 
