Please wait a minute...
Chin. Phys. B, 2023, Vol. 32(3): 038901    DOI: 10.1088/1674-1056/ac7bfa

Topological phase transition in network spreading

Fuzhong Nian(年福忠) and Xia Zhang(张霞)
School of Computer&Communication, Lanzhou University of Technology, Lanzhou 730050, China
Abstract  This paper investigates information spreading from the perspective of topological phase transition. Firstly, a new hybrid network is constructed based on the small-world networks and scale-free networks. Secondly, the attention mechanism of online users in information spreading is studied from four aspects: social distance, individual influence, content richness, and individual activity, and a dynamic evolution model of connecting with spreading is designed. Eventually, numerical simulations are conducted in three types of networks to verify the validity of the proposed dynamic evolution model. The simulation results show that topological structure and node influence in different networks have undergone phase transition, which is consistent with the phenomenon that followers and individual influence in real social networks experience phase transition within a short period. The infection density of networks with the dynamic evolution rule changes faster and reaches higher values than that of networks without the dynamic evolution rule. Furthermore, the simulation results are compared with the real data, which shows that the infection density curve of the hybrid networks is closer to that of the real data than that of the small-world networks and scale-free networks, verifying the validity of the model proposed in this paper.
Keywords:  social network      information spreading      network structure      phase transition  
Received:  26 April 2022      Revised:  30 May 2022      Accepted manuscript online:  27 June 2022
PACS:  89.75.Hc (Networks and genealogical trees)  
  89.75.Fb (Structures and organization in complex systems) (Networks)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61863025 and 62266030), Program for International S & T Cooperation Projects of Gansu Province of China (Grant No. 144WCGA166), and Program for Longyuan Young Innovation Talents and the Doctoral Foundation of LUT.
Corresponding Authors:  Fuzhong Nian     E-mail:

Cite this article: 

Fuzhong Nian(年福忠) and Xia Zhang(张霞) Topological phase transition in network spreading 2023 Chin. Phys. B 32 038901

[1] Newman M E 2003 SIAM Rev. 45 167
[2] Boccaletti S, Latora V, Moreno Y, Chavez M and Hwang D U 2006 Phys. Rep. 424 175
[3] Wang X F and Chen G 2003 IEEE Circ. Syst. Mag. 3 6
[4] Gallos L K, Song C and Makse H A 2007 Physica A 386 686
[5] Pastor-Satorras R, Castellano C, Van Mieghem P and Vespignani A 2015 Rev. Mod. Phys. 87 925
[6] Arenas A, Diaz-Guilera A, Kurths J, Moreno Y and Zhou C 2008 Phys. Rep. 469 93
[7] Pei S, Muchnik L, Andrade Jr J S, Zheng Z and Makse H A 2014 Sci. Rep. 4 5547
[8] Stieglitz S and Dang-Xuan L 2013 J. Manage. Inform. Syst. 29 217
[9] Karsai M, Kivela M, Pan R K, Kaski K, Kertesz J, Barabasi A L and Saramaki J 2011 Phys. Rev. E 83 025102
[10] Li C, Wang L, Sun S and Xia C 2018 Appl. Math. Comput. 320 512
[11] Wang T, Zhou M Y and Fu Z Q 2020 Chin. Phys. B 29 058901
[12] Sun H, Saad D and Lokhov A Y 2021 Phys. Rev. X 11 011048
[13] Leung K, Wu J T and Leung G M 2021 Nat. Commun. 12 1501
[14] Zhao J, Cheng J and Gao H 2014 Seventh International Joint Conference on Computational Sciences and Optimization 2014 325
[15] Lu M, Zhang Z, Qu Z and Kang Y 2018 IEEE Trans. Knowl. Data Eng. 31 1736
[16] Nian F and Dang Z 2018 Int. J. Mod. Phys. B 32 1850106
[17] Nian F, Shi Y and Cao J 2021 J. Comput. Sci. 55 101438
[18] Nian F, Luo L, Yu X and Guo X 2021 Int. J. Mod. Phys. B 35 2150119
[19] Nian F and Liu X 2021 Appl. Intell. 52 889
[20] Wu J, Zheng M, Xu K and Gu C 2020 Nonlinear Dyn. 99 2387
[21] Mheidly N and Fares J 2020 J. Public Health Pol. 41 410
[22] He Z, Cai Z, Yu J, Wang X, Sun Y and Li Y 2017 IEEE Trans. Veh. Technol. 66 2789
[23] Wei X K, Prokhorenko S, Wang B X, Liu Z, Xie Y J, Nahas Y, Jia C L, Dunin-Borkowski R E, Mayer J and Bellaiche L 2021 Nat. commun. 12 1
[24] Perc M 2016 Phys. Lett. A 380 2803
[25] Zurek W H, Dorner U and Zoller P 2005 Phys. Rev. Lett. 95 105701
[26] Kosterlitz J M 2017 Rev. Mod. Phys. 89 040501
[27] Canabarro A, Fanchini F F, Malvezzi A L, Pereira R and Chaves R 2019 Phys. Rev. B 100 045129
[28] Wang W, Liu Q H, Liang J, Hu Y and Zhou T 2019 Phy. Rep. 820 1
[29] Boccaletti S, Almendral J A, Guan S, Leyva I, Liu Z, SendiA-Nadal I, Wang Z and Zou Y 2016 Phys. Rep. 660 1
[30] Li C, Liu F and Li P 2018 Discrete Dyn. Nat. Soc. 2018 1
[31] Xie J, Meng F, Sun J, Ma X, Yan G and Hu Y 2021 Nat. Hum. Behav. 5 1161
[32] Lim S, Jung K and Lui J C 2014 ACM SIGMETRICS Performance Evaluation Review 41 31
[33] Nian F, Yu X, Cao J and Luo L 2020 Int. J. Mod. Phys. B 34 2050203
[34] Davis J T, Perra N, Zhang Q, Moreno Y and Vespignani A 2020 Nat. Phys. 16 590
[35] Zhang S, Wang W, Wu T and Lin T 2019 Physica A 534 122218
[36] Wen X, Yang C, Yang Y P and Chen Y G 2017 Chin. Phys. Lett. 34 058901
[37] Mansouri A and Taghiyareh F 2021 J. Inform. Syst. Tele. 9 1
[38] Holme P and Newman M E 2006 Phys. Rev. E 74 056108
[39] Yu X, Nian F, Yao Y and Luo L 2021 IEEE Trans. Comput. Soc. Syst. 8 1143
[40] Liu H, Zhang Y, Kadir A and Xu Y 2019 Appl. Math. Comput. 360 83
[41] Liu H, Kadir A and Xu C 2020 Int. J. Bifurcat. Chaos 30 2050173
[42] Liu H, Xu Y and Ma C 2020 Optik 216 164925
[43] Watts D J and Strogatz S H 1998 Nature 393 440
[44] Wang X F and Chen G 2002 Int. J. Bifurcat. Chaos 12 187
[45] Barabási A L 2009 Science 325 412
[46] Holme P and Kim B J 2002 Phys. Rev. E 65 026107
[47] Charness G, Haruvy E and Sonsino D 2007 J. Econ. Behav. Organ. 63 88
[48] Boguná M, Pastor-Satorras R, Díaz-Guilera A and Arenas A 2004 Phys. Rev. E 70 056122
[49] Perc M 2014 J. R. Soc. Interface 11 20140378
[1] Tailoring of thermal expansion and phase transition temperature of ZrW2O8 with phosphorus and enhancement of negative thermal expansion of ZrW1.5P0.5O7.75
Chenjun Zhang(张晨骏), Xiaoke He(何小可), Zhiyu Min(闵志宇), and Baozhong Li(李保忠). Chin. Phys. B, 2023, 32(4): 048201.
[2] Liquid-liquid phase transition in confined liquid titanium
Di Zhang(张迪), Yunrui Duan(段云瑞), Peiru Zheng(郑培儒), Yingjie Ma(马英杰), Junping Qian(钱俊平), Zhichao Li(李志超), Jian Huang(黄建), Yanyan Jiang(蒋妍彦), and Hui Li(李辉). Chin. Phys. B, 2023, 32(2): 026801.
[3] Prediction of flexoelectricity in BaTiO3 using molecular dynamics simulations
Long Zhou(周龙), Xu-Long Zhang(张旭龙), Yu-Ying Cao(曹玉莹), Fu Zheng(郑富), Hua Gao(高华), Hong-Fei Liu(刘红飞), and Zhi Ma(马治). Chin. Phys. B, 2023, 32(1): 017701.
[4] Magnetocaloric properties and Griffiths phase of ferrimagnetic cobaltite CaBaCo4O7
Tina Raoufi, Jincheng He(何金城), Binbin Wang(王彬彬), Enke Liu(刘恩克), and Young Sun(孙阳). Chin. Phys. B, 2023, 32(1): 017504.
[5] Configurational entropy-induced phase transition in spinel LiMn2O4
Wei Hu(胡伟), Wen-Wei Luo(罗文崴), Mu-Sheng Wu(吴木生), Bo Xu(徐波), and Chu-Ying Ouyang(欧阳楚英). Chin. Phys. B, 2022, 31(9): 098202.
[6] Hard-core Hall tube in superconducting circuits
Xin Guan(关欣), Gang Chen(陈刚), Jing Pan(潘婧), and Zhi-Guo Gui(桂志国). Chin. Phys. B, 2022, 31(8): 080302.
[7] Exchange-coupling-induced fourfold magnetic anisotropy in CoFeB/FeRh bilayer grown on SrTiO3(001)
Qingrong Shao(邵倾蓉), Jing Meng(孟婧), Xiaoyan Zhu(朱晓艳), Yali Xie(谢亚丽), Wenjuan Cheng(程文娟), Dongmei Jiang(蒋冬梅), Yang Xu(徐杨), Tian Shang(商恬), and Qingfeng Zhan(詹清峰). Chin. Phys. B, 2022, 31(8): 087503.
[8] Effect of f-c hybridization on the $\gamma\to \alpha$ phase transition of cerium studied by lanthanum doping
Yong-Huan Wang(王永欢), Yun Zhang(张云), Yu Liu(刘瑜), Xiao Tan(谈笑), Ce Ma(马策), Yue-Chao Wang(王越超), Qiang Zhang(张强), Deng-Peng Yuan(袁登鹏), Dan Jian(简单), Jian Wu(吴健), Chao Lai(赖超), Xi-Yang Wang(王西洋), Xue-Bing Luo(罗学兵), Qiu-Yun Chen(陈秋云), Wei Feng(冯卫), Qin Liu(刘琴), Qun-Qing Hao(郝群庆), Yi Liu(刘毅), Shi-Yong Tan(谭世勇), Xie-Gang Zhu(朱燮刚), Hai-Feng Song(宋海峰), and Xin-Chun Lai(赖新春). Chin. Phys. B, 2022, 31(8): 087102.
[9] Characterization of topological phase of superlattices in superconducting circuits
Jianfei Chen(陈健菲), Chaohua Wu(吴超华), Jingtao Fan(樊景涛), and Gang Chen(陈刚). Chin. Phys. B, 2022, 31(8): 088501.
[10] Structural evolution and molecular dissociation of H2S under high pressures
Wen-Ji Shen(沈文吉), Tian-Xiao Liang(梁天笑), Zhao Liu(刘召), Xin Wang(王鑫), De-Fang Duan(段德芳), Hong-Yu Yu(于洪雨), and Tian Cui(崔田). Chin. Phys. B, 2022, 31(7): 076102.
[11] Structural evolution and bandgap modulation of layered β-GeSe2 single crystal under high pressure
Hengli Xie(谢恒立), Jiaxiang Wang(王家祥), Lingrui Wang(王玲瑞), Yong Yan(闫勇), Juan Guo(郭娟), Qilong Gao(高其龙), Mingju Chao(晁明举), Erjun Liang(梁二军), and Xiao Ren(任霄). Chin. Phys. B, 2022, 31(7): 076101.
[12] Topological phase transition in cavity optomechanical system with periodical modulation
Zhi-Xu Zhang(张志旭), Lu Qi(祁鲁), Wen-Xue Cui(崔文学), Shou Zhang(张寿), and Hong-Fu Wang(王洪福). Chin. Phys. B, 2022, 31(7): 070301.
[13] Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model
Yan-Wei Dai(代艳伟), Sheng-Hao Li(李生好), and Xi-Hao Chen(陈西浩). Chin. Phys. B, 2022, 31(7): 070502.
[14] Influence fast or later: Two types of influencers in social networks
Fang Zhou(周方), Chang Su(苏畅), Shuqi Xu(徐舒琪), and Linyuan Lü(吕琳媛). Chin. Phys. B, 2022, 31(6): 068901.
[15] Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions
Kaiyuan Cao(曹凯源), Ming Zhong(钟鸣), and Peiqing Tong(童培庆). Chin. Phys. B, 2022, 31(6): 060505.
No Suggested Reading articles found!