Network topology of renewable energy companies: minimal spanning tree and sub-dominant ultrametric for the American stock

    Mansooreh Kazemilari Affiliation
    ; Ali Mohamadi Affiliation
    ; Abbas Mardani Affiliation
    ; Justas Streimikis Affiliation


Renewable energy has become a significant market player after the turn of the millennium. Wind, solar, smart grid and further renewable energy stocks have experienced both serious up and down trends since that time. In this paper, computed the Minimal Spanning Tree (MST) and Sub-Dominant Ultrametric (SDU) for topological properties of what has been driving the price of renewable energy stock markets and sectors. In this regard, the main object is to define the similarity among sectors in financial market, which is statistically a multivariate time series. The principal mathematical tool to do macro analysis is multivariate vector correlation where multi-dimensional data is considered as a complex system. Furthermore, the base approach for filtering the significant information in a financial system is similarity network analysis. In this paper, the behavior of economic sectors of renewable energy played during 30th July 2015 – 1th January 2018 in America. Results of this study found that, solar sector in renewable energy is confirmed as the dominant sector in America during this period. In addition, results demonstrated that, the leader sector is Solar and the central hubs are Canadian Solar Inc. (CSIQ)from Solar and then Pattern Energy Group Inc. (PEGI)from Solar-Wind sectors.

Keyword : sector analysis, renewable energy, stock market, Similarity network analysis

How to Cite
Kazemilari, M., Mohamadi, A., Mardani, A., & Streimikis, J. (2019). Network topology of renewable energy companies: minimal spanning tree and sub-dominant ultrametric for the American stock. Technological and Economic Development of Economy, 25(2), 168-187.
Published in Issue
Feb 7, 2019
Abstract Views
PDF Downloads
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.


Abbasi, A., & Altmann, J. (2011). On the correlation between research performance and social network analysis measures applied to research collaboration networks. In 44th Hawaii International Conference on System Sciences (HICSS), 4–7 January 2011, Kauai, HI, USA (pp. 1-10). IEEE.

Albert, R., & Barabási, A.-L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74(1), 47.

Batagelj, V., & Mrvar, A. (2003). Density based approaches to network analysis – Analysis of Reuters terror news network. 20 p.

Batagelj, V., & Mrvar, A. (2004). Pajekanalysis and visualization of large networks. Springer.

Borgatti, S. P. (2005). Centrality and network flow. Social Networks, 27(1), 55-71.

Borgatti, S. P. (2006). Identifying sets of key players in a social network. Computational & Mathematical Organization Theory, 12(1), 21-34.

Borgatti, S. P., & Everett, M. G. (2006). A Graph-theoretic perspective on centrality. Social Networks, 28(4), 466-484.

Borgatti, S. P., Carley, K. M., & Krackhardt, D. (2006). On the robustness of centrality measures under conditions of imperfect data. Social Networks, 28(2), 124-136.

Brida, J. G., & Risso, W. A. (2010). Hierarchical structure of the German stock market. Expert Systems with Applications, 37(5), 3846-3852.

Chang, M.-Ch., & Shieh, H.-Sh. (2017). The relations between energy efficiency and GDP in the Baltic Sea Region and Non-Baltic Sea Region. Transformations in Business & Economics, 16(2(41), 235-247.

Coxhead, P. (1974). Measuring the relationship between two sets of variables. British Journal of Mathematical and Statistical Psychology, 27(2), 205-212.

Cramer, E. M., & Nicewander, W. A. (1979). Some symmetric, invariant measures of multivariate association. Psychometrika, 44(1), 43-54.

De Nooy, W., Mrvar, A., & Batagelj, V. (2011). Exploratory social network analysis with Pajek (Vol. 27). Cambridge University Press.

Djauhari, M. A. (2012). A robust filter in stock networks analysis. Physica A: Statistical Mechanics and its Applications, 391(20), 5049-5057.

Dutta, A., Bouri, E., & Noor, M. H. (2018). Return and volatility linkages between CO2 emission and clean energy stock prices. Energy, 164, 803-810.

Eom, C., Oh, G., & Kim, S. (2008). Statistical investigation on connected structure of stock networks in a financial time series. Korean Physical Society, 53, 3837-3841.

Escoufier, Y. (1973). Le traitement des variables vectorielles. Biometrics, 29(4), 751-760.

Espino, J. M., & Hoyos, J. R. C. (2010). Stability of centrality measures in social network analyses to identify long-lasting leaders from an indigenous boarding school of northern Mexico. Estudios Sobre las Culturas Contempor´aneas, 32, 155-171.

Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 40(1), 35-41.

Freeman, L. C. (1979). Centrality in social networks conceptual clarification. Social Networks, 1(3), 215-239.

Garas, A., & Argyrakis, P. (2007). Correlation study of the Athens stock exchange. Physica A: Statistical Mechanics and its Applications, 380, 399-410.

Gormus, N. A., Soytas, U., & Diltz, J. D. (2015). Oil prices, fossil-fuel stocks and alternative energy stocks. International Journal of Economics and Finance, 7(7), 43-55.

Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28(3-4), 321-377.

Investopedia. (2018). Retrieved from

Jang, W., Lee, J., & Chang, W. (2011). Currency crises and the evolution of foreign exchange market: Evidence from minimum spanning tree. Physica A: Statistical Mechanics and its Applications, 390(4), 707-718.

Jovovic, R., Simanaviciene, Z., & Dirma, V. (2017). Assessment of heat production savings resulting from replacement of gas with biofuels. Transformations in Business & Economics, 16(1), 34-51.

Kantar, E., Keskin, M., & Deviren, B. (2012). Analysis of the effects of the global financial crisis on the Turkish economy, using hierarchical methods. Physica A: Statistical Mechanics and its Applications, 391(7), 2342-2352.

Kazemilari, M., & Djauhari, M. A. (2015). Correlation network analysis for multi-dimensional data in stocks market. Physica A: Statistical Mechanics and its Applications, 429, 62-75.

Kazemilari, M., Mardani, A., Streimikiene, D., & Zavadskas, E. K. (2017). An overview of renewable energy companies in stock exchange: Evidence from minimal spanning tree approach. Renewable Energy, 102(Part A), 107-117.

Kruskal, J. B. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society, 7(1), 48-50.

Kshirsagar, A. (1969). Correlation between two vector variables. Journal of the Royal Statistical Society. Series B (Methodological), 31(3), 477-485.

Kwapień, J, & Drożdż, S. (2012). Physical approach to complex systems. Physics Reports, 515(3), 115-226.

Lyu, X., & Shi, A. (2018). Research on the renewable energy industry financing efficiency assessment and mode selection. Sustainability, 10(1), 222.

Mantegna, R. N. (1999). Hierarchical structure in financial markets. The European Physical Journal B-Condensed Matter and Complex Systems, 11(1), 193-197.

Mantegna, R. N., & Stanley, H. E. (1999). Introduction to econophysics: correlations and complexity in finance. Cambridge University Press.

Mantegna, R., & Stanley, H. E. (2000). An introduction to econophysics. Cambridge, MA: Cambridge University Press.

Masuyama, M. (1941). Correlation coefficient between two sets of complex vectors. Proceedings of the Physico-Mathematical Society of Japan. 3rd Series 23, 918-924.

Micciche, S., Bonanno, G., Lillo, F., & Mantegna, R. N. (2003). Degree stability of a minimum spanning tree of price return and volatility. Physica A: Statistical Mechanics and its Applications, 324(1-2), 66-73.

Mundada, A. S., Prehoda, E. W, Pearce, J. M. (2017). U. S. market for solar photovoltaic plug-and-play systems. Renewable Energy, 103, 255-264.

Newman, M. E. (2005). A measure of betweenness centrality based on random walks. Social Networks, 27(1), 39-54.

New York Stock Exchange [NYSE]. (n.d.). Retrieved from

Onnela, J.-P., Chakraborti, A., Kaski, K., Kertesz, J., & Kanto, A. (2003). Dynamics of market correlations: Taxonomy and portfolio analysis. Physical Review E, 68(5), 056110.

Park, K., & Yilmaz, A. (2010, April 26-30). A social network analysis approach to analyze road networks. ASPRS Annual Conference (pp. 1-6). San Diego, California, CA.

Renewable Energy World. (2018). Renewable Energy News & Information. Retrieved from

Robert, P., & Escoufier, Y. (1976). A unifying tool for linear multivariate statistical methods: the RV-coefficient. Applied Statistics, 25(3), 257-265.

Rosenow, B., Gopikrishnan, P., Plerou, V., & Stanley, H. E. (2003). Dynamics of cross-correlations in the stock market. Physica A: Statistical Mechanics and its Applications, 324(1), 241-246.

Ross, S. M. (2011). An elementary introduction to mathematical finance. Cambridge University Press.

Shaffer, J. P., & Gillo, M. W. (1974). A multivariate extension of the correlation ratio. Educational and Psychological Measurement, 34(3), 521-524.

Sieczka, P., & Hołyst, J. A. (2009). Correlations in commodity markets. Physica A: Statistical Mechanics and its Applications, 388(8), 1621-1630.

Stephens, M. (1979). Vector correlation. Biometrika, 66(1), 41-48.

Stürmer, B., Novakovits, Ph., Luidolt, A., & Zweiler, R. (2019). Potential of renewable methane by anaerobic digestion from existing plant stock – An economic reflection of an Austrian region. Renewable Energy, 130, 920-929.

Tabak, B. M., Serra, T. R., & Cajueiro, D. O. (2010). Topological properties of stock market networks: The case of Brazil. Physica A: Statistical Mechanics and its Applications, 389(16), 3240-3249.

Tola, V., Lillo, F., Gallegati, M., & Mantegna, R. N. (2008). Cluster analysis for portfolio optimization. Journal of Economic Dynamics and Control, 32(1), 235-258.

Tumminello, M., Aste, T., Di Matteo, T., & Mantegna, R. N. (2005). A tool for filtering information in complex systems. Proceedings of the National Academy of Sciences of the United States of America, 102(30), 10421-10426.

Ulusoy, T., Keskin, M., Shirvani, A., Deviren, B., Kantar, E., & D¨onmez, C. C. (2012). Complexity of major UK companies between 2006 and 2010: Hierarchical structure method approach. Physica A: Statistical Mechanics and its Applications, 391(21), 5121-5131.

Wang, G.-J., Xie, C., Han, F., & Sun, B. (2012). Similarity measure and topology evolution of foreign exchange markets using dynamic time warping method: Evidence from minimal spanning tree. Physica A: Statistical Mechanics and its Applications, 391(16), 4136-4146.

Xu, Y., Ma, J., Sun, Y., Hao, J., Sun, Y., & Zhao, Y. (2009). Using social network analysis as a strategy for e-commerce recommendation. PACIS 2009 Proceedings, 106. Retrieved from

Yahoo Finance. (n.d.). Retrieved from

Zeng, S., Jiang, C., Ma, C., & Su, B. (2018). Investment efficiency of the new energy industry in China. Energy Economics, 70, 536-544.

Zhang, G., & Du, Z. (2017). Co-movements among the stock prices of new energy, high-technology and fossil fuel companies in China. Energy, 135, 249-256.

Zhang, H., Zhang, X., Sun, Y., Liu, J., Li, W., & Tian, J. (2011b). A weighted-RV method to detect fine-scale functional connectivity during resting state. NeuroImage, 54(4), 2885-2898.

Zhang, Y., Lee, G. H. T., Wong, J. C., Kok, J. L., Prusty, M., & Cheong, S. A. (2011a). Will the US economy recover in 2010? A minimal spanning tree study. Physica A: Statistical Mechanics and its Applications, 390(11), 2020-2050.