Abstract：Based on the 2017 Hangzhou electricity consumption data of industrial enterprises, this paper aims to establish correlation networks to filter out the central enterprises and their connections in the city. First, we exclude the seasonal effect on electricity consumption and calculate the pure correlation of these enterprises by using the conditional Pearson correlation model. Next, we adjust the correlation coefficient thresholds by making the node degree distribution approximately satisfy the power-law distributions. Then, the empirical analysis on network properties is carried out, including the heavy-head distribution, the assortative mixing, and the small-world property. Based on these properties, we propose an approach for identifying central enterprises in the electricity consumption correlation network. The study shows that the central enterprises are closely related and can promote the connection between other non-central enterprises. Decision-makers can regulate the central enterprises detected by our approach in order to affect the overall development of the city.
许荣华, 胡仁杰, 綦方中, 马庆国. 基于幂律特性的企业用电量网络构建与中心企业分析[J]. 复杂系统与复杂性科学, 2021, 18(1): 38-47.
XU Ronghua, HU Renjie, QI Fangzhong, MA Qingguo. Network Modeling and Central Node Analysis of Enterprise Correlations in Terms of Electricity Consumption Based on Power-Law Distribution. Complex Systems and Complexity Science, 2021, 18(1): 38-47.
[1] 刘涤尘,冀星沛,王波,等.基于复杂网络理论的电力通信网拓扑脆弱性分析及对策[J]. 电网技术, 2015, 39(12):325331. Liu Dichen, Ji Xipei, Wang Bo, et al. Analysis and countermeasures of topological vulnerability of power communication network based on complex network theory[J]. Grid Technology, 2015, 39(12):325331. [2] Zhou Y, Zhang S S, Wu L B, et al. Predicting sectoral electricity consumption based on complex network analysis[J]. Applied Energy, 2019, 255(S1):113790. [3] Yao C Z, Lin J N, Lin Q W, et al. A study of causality structure and dynamics in industrial electricity consumption based on Granger network[J]. Physica A: Statistical Mechanics and Its Applications, 2016, 462:297320. [4] Yao C Z, Lin J N, Liu X F. A study of hierarchical structure on South China industrial electricity-consumption correlation[J]. Physica A: Statistical Mechanics and Its Applications, 2016, 444: 129145. [5] Yao C Z, Lin Q W, Lin J N. A study of industrial electricity consumption based on partial Granger causality network[J]. Physica A: Statistical Mechanics and Its Applications, 2016, 461:629646. [6] Granger C W. Investigating causal relations by econometric models and cross-spectral methods[J]. Econometrica, 1969, 37(3):424438. [7] Krishna R, Guo S. A partial granger causality approach to explore causal networks derived from multi-parameter data[C]//Proceedings of the 6th International Conference on Computational Methods in Systems Biology, Rostock, Germany, 2008:927. [8] Tumminello M, Lillo F, Mantegna R N. Correlation, hierarchies, and networks in financial markets[J]. Journal of Economic Behavior & Organization, 2009, 75(1):4058. [9] Xiao B Q, Yang Y, Peng X R, et al.Measuring the connectedness of European electricity markets using the network topology of variance decompositions[J]. Physica A: Statistical Mechanics and its Applications, 2019, 535:122279. [10] Kantar E, Keskin M. The relationships between electricity consumption and GDP in Asian countries, using hierarchical structure methods[J]. Physica A: Statistical Mechanics and Its Applications, 2013, 392(22):56785684. [11] Tang Y, Xiong J J, Jia Z Y, et al. Complexities in financial network topological dynamics: modeling of emerging and developed stock markets[J]. Complexity, 2018:131. [12] Hu S, Yang H, Cai B, et al. Research on spatial economic structure for different economic sectors from a perspective of a complex network[J]. Physica A: Statistical Mechanics and Its Applications, 2013, 392(17):36823697. [13] Li X, Jin Y Y, Chen G. Complexity and synchronization of the World trade Web[J]. Physica A: Statistical Mechanics and its Applications, 2003, 328(12):287296. [14] Lee K M, Yang J S, Kim G, et al. Impact of the topology of global macroeconomic network on the spreading of economic crises[J]. PLoS One, 2011, 6(3):e18443. [15] Flake G W, Lawrence S, Giles C L, et al. Self-organization and identification of web communities[J]. Computer, 2002, 35(3):6670. [16] Clauset A, Shalizi C R, Newman M E J. Power-law distributions in empirical data[J]. Annals of Applied Statistics, 2012, 8(1):89119. [17] Yamamoto Y, Yokoyama K. Common and unique network dynamics in football games[J]. PLoS One, 2011,6(12):e29638. [18] Yang Y, Yang H. Complex network-based time series analysis[J]. Physica A: Statistical Mechanics and Its Applications, 2008, 387(56):13811386. [19] Newman M E J. Power laws, paretodistributions and Zipf’s law[J]. Contemporary Physics, 2005, 46(5):323351. [20] Lorenz M O. Methods of measuring the concentration of wealth[J]. Publications of the American Statistical Association, 1905, 9(70):209219. [21] Calderón C, Lin L. The direction of causality between financial development and economic growth[J]. Journal of Development Economics, 2003, 72(1):321334. [22] Bland J M, Altman D G. Statistical methods for assessing agreement between two methods of clinical measurement[J]. International Journal of Nursing Studies, 1986, 327(8476):307. [23] Morck R, Yeung B, Yu W. The information content of stock markets: why do emerging markets have synchronous stock price movements? [J]. Journal of Financial Economics, 2000, 58(1):215260. [24] Moore D S, Notz W I, Notz W.Statistics: Concepts and Controversies[M]. London: Macmillan, 2006. [25] Lu E T, Hamilton R J. Avalanches and the distribution of solar flares[J]. The Astrophysical Journal, 1991, 380(2):8992. [26] Florence P S, Zipf G K. Human behaviour and the principle of least effort[J]. The Economic Journal, 1950, 60(240):808810. [27] Achlioptas D, Clauset A, Kempe D, et al. On the bias of traceroute sampling: or, power-law degree distributions in regular graphs[J]. Journal of the Association for Computing Machinery, 2009, 56(4):128. [28] Reed W J. The Pareto, Zipf and other power laws[J]. Economics Letters, 2001, 74(1):1519. [29] Moody J. Race, school integration, and friendship segregation in America[J]. American Journal of Sociology,2001, 107(3):679716. [30] Abbasi A, Altmann J, Hossain L. Identifying the effects of co-authorship networks on the performance of scholars: a correlation and regression analysis of performance measures and social network analysis measures[J]. Journal of Informetrics, 2011, 5(4):594607. [31] Bonacich P. Power and centrality: a family of measures[J]. American Journal of Sociology, 1987, 92(5):11701182. [32] Yong L U, Polgar M, Luo X, et al. Social network analysis of a criminal hacker community[J]. Journal of Computer Information Systems, 2010, 51(2):3141. [33] Milgram S. The small world problem[J]. Psychology Today, 1967, 2(1):6167.
