Fluctuation behavior of the evolution of complex networks

doi:10.3969/j.issn.1000-5641.2022.04.015

Abstract

Abstract:

Research on complex networks has given birth to models for understanding evolution dynamics and structure formation; their respective degree growth fluctuations, however, behave very differently. To test the validity of existing models, we carry out an empirical study on two real networks. The results show that both their fluctuation exponents decrease linearly with the observation interval, presenting an interval-dependent picture that has not been predicted by any of the existing models. By exploring the response of the fluctuation to shuffling data, we deduce the interval dependence from the reinforcement of the internal temporal correlation. These results reveal not only the limitations of the existing models, but the complex dynamics of the correlation itself, which is significant for further understanding the underlying mechanism of network evolution.

Key words: degree growth, fluctuation, Gibrat’s law, correlation

CLC Number:

O415.6

Qichen LIU, Jianghai QIAN, Hanyun CHANG. Fluctuation behavior of the evolution of complex networks[J]. Journal of East China Normal University(Natural Science), 2022, 2022(4): 147-153.

Figures/Tables 3

References 32

1	BOCCALETTI S, LATORA V, MORENO Y, et al. Complex networks: Structure and dynamics. Physics Reports, 2006, 424 (4/5): 175- 308.
2	NEWMAN M E J. The structure and function of complex networks. Society for Industrial and Applied Mathematics (SIAM) Review, 2003, 45 (2): 167- 256.
3	COSTA L F, RODRIGUES F A, TRAVIESO G, et al. Characterization of complex networks: A survey of measurements. Advances in Physics, 2007, 56 (1): 167- 242.
4	COSTA L F, OLIVEIRA JR O N, TRAVIESO G, et al. Analyzing and modeling real-world phenomena with complex networks: A survey of applications. Advances in Physics, 2011, 60 (3): 329- 412.
5	BARABÁSI A L, ALBERT R. Emergence of scaling in random networks. Science, 1999, 286 (5439): 509- 512.
6	MITZENMACHER M. A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 2004, 1 (2): 226- 251.
7	BIANCONI G, BARABÁSI A L. Bose-Einstein condensation in complex networks. Physical Review Letters, 2001, 86 (24): 5632-5635.
8	FORTUNATO S, FLAMMINI A, MENCZER F. Scale-free network growth by ranking. Physical Review Letters, 2006, 96 (21): 218701.
9	WANG W X, WANG B H, HU B, et al. General dynamics of topology and traffic on weighted technological networks. Physical Review Letters, 2005, 94 (18): 188702.
10	KUMPULA J M, ONNELA J P, SARAMÄKI J, et al. Emergence of communities in weighted networks. Physical Review Letters, 2007, 99 (22): 228701.
11	QIAN J H, ZHAO S T, XU J. Emergence of double power-law degree distribution by controlling the evolution of BA model. Physica A, 2021, 562, 125333.
12	徐静, 钱江海. 动态空间约束网络模型及其双段幂律特征. 复杂系统与复杂性科学, 2020, 17 (3): 86- 93.
13	JEONG H, NÉDA Z, BARABÁSI A L. Measuring preferential attachment in evolving networks. Europhysics Letters, 2003, 61 (4): 567-572.
14	CAPOCCI A, SERVEDIO V D P, COLAIORI F, et al. Preferential attachment in the growth of social networks: The internet encyclopedia Wikipedia. Physical Review E, 2006, 74 (3): 036116.
15	WANG M Y, YU G, YU D R. Measuring the preferential attachment mechanism in citation networks. Physica A, 2008, 387 (18): 4692- 4698.
16	ROZENFELD H D, RYBSKI D, ANDRADE J S, et al. Laws of population growth. Proceedings of the National Academy of Sciences (PNAS), 2008, 105 (48): 18702- 18707.
17	STANLEY M H R, AMARAL L A N, BULDYREV S V, et al. Scaling behaviour in the growth of companies. Nature, 1996, 379 (6568): 804- 806.
18	LEE Y, AMARAL L A N, CANNING D, et al. Universal features in the growth dynamics of complex organizations. Physical Review Letters, 1998, 81 (15): 3275.
19	PLEROU V, AMARAL L A N, GOPIKRISHNAN P, et al. Similarities between the growth dynamics of university research and of competitive economic activities. Nature, 1999, 400 (6743): 433- 437.
20	RICCABONI M, PAMMOLLI F, BULDYREV S V, et al. The size variance relationship of business firm growth rates [J]. Proceedings of the National Academy of Sciences (PNAS) 2008, 105(50): 19595-19600.
21	FU D F, PAMMOLLI F, BULDYREV S V, et al. The growth of business firms: Theoretical framework and empirical evidence. Proceedings of the National Academy of Sciences (PNAS), 2005, 102 (52): 18801- 18806.
22	HUBERMAN B A, ADAMIC L A. Growth dynamics of the World-Wide Web. Nature, 1999, 401 (6749): 131.
23	GOH K I, KAHNG B, KIM D. Fluctuation-driven dynamics of the Internet topology. Physical Review Letters, 2002, 88 (10): 108701.
24	GAUTREAU A, BARRAT A, BARTHÉLEMY M. Microdynamics in stationary complex networks. Proceedings of the National Academy of Sciences, 2009, 106 (22): 8847- 8852.
25	RYBSKI D, BULDYREV S V, HAVLIN S, et al. Scaling laws of human interaction activity. Proceedings of the National Academy of Sciences, 2009, 106 (31): 12640- 12645.
26	RYBSKI D, BULDYREV S V, HAVLIN S, et al. Communication activity in a social network: Relation between long-term correlations and inter-event clustering [J]. Scientific Reports, 2012(2): 560. DOI: 10.1038/srep00560.
27	RYBSKI D, BULDYREV S V, HAVLIN S, et al. Communication activity in social networks: Growth and correlations. The European Physical Journal B, 2011, 84 (1): 147- 159.
28	AYDOGAN Y, DONDURAN M. Concluding Gibrat’s law with Turkish firm data. Physica A, 2019, 533, 122066.
29	ISHIKAWA A, FUJIMOTO S, RAMOS A, et al. Initial value dependence of urban population’s growth-rate distribution and the long-term growth [J]. Frontiers in Physics, 2020(8): 302. DOI: 10.3389/fphy.2020.00302.
30	XU Y, WANG Y G, TAO X B, et al. Evidence of Chinese income dynamics and its effects on income scaling law. Physica A, 2017, 487, 143- 152.
31	ZHU K L, LI W Z, FU X M, et al. How do online social networks grow?. PloS One, 2014, 9 (6): e100023.
32	KUNEGIS J. Konect: The koblenz network collection [C]// Proceedings of the 22nd International Conference on World Wide Web. 2013: 1343-1350.

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