{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:19:04Z","timestamp":1760059144517,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,5,25]],"date-time":"2025-05-25T00:00:00Z","timestamp":1748131200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2021MF133","ZR2022MF278","72174091","K20231036","2023r046"],"award-info":[{"award-number":["ZR2021MF133","ZR2022MF278","72174091","K20231036","2023r046"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["ZR2021MF133","ZR2022MF278","72174091","K20231036","2023r046"],"award-info":[{"award-number":["ZR2021MF133","ZR2022MF278","72174091","K20231036","2023r046"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"\u201cTaihu Light\u201d Science and Technology Project of Wuxi","award":["ZR2021MF133","ZR2022MF278","72174091","K20231036","2023r046"],"award-info":[{"award-number":["ZR2021MF133","ZR2022MF278","72174091","K20231036","2023r046"]}]},{"name":"Wuxi University Research Start-up Fund for Introduced Talents","award":["ZR2021MF133","ZR2022MF278","72174091","K20231036","2023r046"],"award-info":[{"award-number":["ZR2021MF133","ZR2022MF278","72174091","K20231036","2023r046"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As an essential chemical raw material and a cost-effective energy product, fluctuations in propane price has garnered significant attention in the energy market. This paper processes the original time series using a coarse-grained method and employs symbolic representation combined with the sliding window technique to represent fluctuation modes as nodes within a network. The weight and direction of the edges among the nodes are determined by the number and direction of the conversions among the modes, thereby mapping the original sequence of the propane price into the propane price oriented weighted network (PPOWN) by the symbolic patterns, which is an asymmetric network that has evolved from the symmetric network based on symmetry theory. The results indicate that the core fluctuation state of the PPOWN is concentrated in the first 0.96% of the nodes, exhibiting scale-free network characteristics and dynamic asymmetry. Nodes with greater strength are more closely interconnected, but not all early-appearing nodes possess great strength. The PPOWN demonstrates a short-range correlation (L\u00af=8.5405) and a highly linear growth trend in the cumulative time interval of the new nodes. Additionally, the nodes of the PPOWN display low betweenness, clustering coefficient, and strength, which significantly differ from the random and chaotic networks. The presence of these lower-strength nodes often signifies that the market is undergoing a transformation or transition period. By identifying and analyzing these nodes, subsequent propane price fluctuations can be predicted more effectively, enhancing market responsiveness.<\/jats:p>","DOI":"10.3390\/sym17060821","type":"journal-article","created":{"date-parts":[[2025,5,25]],"date-time":"2025-05-25T20:39:36Z","timestamp":1748205576000},"page":"821","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analysis of the Propane Price Oriented Weighted Network Based on the Symbolic Pattern Representation of Time Series"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4803-9022","authenticated-orcid":false,"given":"Guangyong","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of General Education, Wuxi University, Wuxi 214105, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Digital Economics and Management, Wuxi University, Wuxi 214105, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiangtao","family":"Yuan","sequence":"additional","affiliation":[{"name":"Department of General Education, Wuxi University, Wuxi 214105, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zifang","family":"Qu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133656","DOI":"10.1016\/j.energy.2024.133656","article-title":"Asymmetric relationship between carbon market and energy markets","volume":"313","author":"Abakah","year":"2024","journal-title":"Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"100140","DOI":"10.1016\/j.egycc.2024.100140","article-title":"Fossil fuel prices and economic policy uncertainty\u2013A regime-switching approach","volume":"5","author":"Ayinde","year":"2024","journal-title":"Energy Clim. Change"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105008","DOI":"10.1016\/j.resourpol.2024.105008","article-title":"Fossil energy market price prediction by using machine learning with optimal hyper-parameters, A comparative study","volume":"92","author":"Lahmiri","year":"2024","journal-title":"Resour. Policy"},{"key":"ref_4","unstructured":"Hamilton, J.D. (1994). Time Series Analysi, Princeton University Press."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1002\/fut.20120","article-title":"Volatility and commodity price dynamics","volume":"24","author":"Pindyck","year":"2004","journal-title":"J. Futures Mark."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.energy.2014.01.077","article-title":"Energy price dynamics in the US market. Insights from a heterogeneous multi-regime framework","volume":"68","author":"Dias","year":"2014","journal-title":"Energy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1080\/15567249.2019.1607631","article-title":"Effects of the shale boom on ethylene and propylene prices","volume":"14","author":"Kim","year":"2019","journal-title":"Energy Sources Part B Econ. Plan. Policy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.enpol.2015.01.003","article-title":"Oil prices and financial stress: A volatility spillover analysis","volume":"82","author":"Nazlioglu","year":"2015","journal-title":"Energy Policy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"109765","DOI":"10.1016\/j.econlet.2021.109765","article-title":"An aggregate test for transient market power in the winter 2013\u201314 propane market","volume":"200","author":"Moul","year":"2021","journal-title":"Econ. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.apenergy.2012.10.066","article-title":"Investigating the price discovery and risk transfer functions in the crude oil and gasoline futures markets: Some empirical evidence","volume":"104","author":"Zhang","year":"2013","journal-title":"Appl. Energy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"315","DOI":"10.32479\/ijeep.9631","article-title":"Identifying the dynamic connectedness between propane and oil prices, Evidence from wavelet analysis","volume":"10","author":"Hung","year":"2020","journal-title":"Int. J. Energy Econ. Policy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"102035","DOI":"10.1016\/j.najef.2023.102035","article-title":"Dynamic volatility spillover among cryptocurrencies and energy markets: An empirical analysis based on a multilevel complex network","volume":"69","author":"Wang","year":"2024","journal-title":"North Am. J. Econ. Financ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"121896","DOI":"10.1016\/j.energy.2021.121896","article-title":"Characterizing the dynamic evolutionary behavior of multivariate price movement fluctuation in the carbon-fuel energy markets system from complex network perspective","volume":"239","author":"Chen","year":"2022","journal-title":"Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/978-3-319-13153-5_3","article-title":"An ensemble CRT, RVFLN, SVM method for estimating propane spot price","volume":"331","author":"Chiroma","year":"2015","journal-title":"Adv. Intell. Syst. Comput."},{"key":"ref_15","first-page":"63","article-title":"Networks for systems biology, conceptual connection of data and function","volume":"6","author":"Dehmer","year":"2012","journal-title":"IET Syst. Biol."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Mantegna, R.N., and Stanley, H.E. (1999). Introduction to Econophysics, Correlations and Complexity in Finance, Cambridge University Press.","DOI":"10.1017\/CBO9780511755767"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"121824","DOI":"10.1016\/j.ins.2024.121824","article-title":"Stock complex networks based on the GA-LightGBM model: The prediction of firm performance","volume":"700","author":"Huang","year":"2025","journal-title":"Inf. Sci."},{"key":"ref_18","first-page":"104878","article-title":"Crude oil price analysis and forecasting based on complex network theory","volume":"91","author":"He","year":"2020","journal-title":"Energy Econ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"108871","DOI":"10.1016\/j.asoc.2022.108871","article-title":"Electric demand forecasting with neural networks and symbolic time series representations","volume":"122","author":"Pegalajar","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.apenergy.2010.07.034","article-title":"Investigating price clustering in the oil futures market","volume":"88","author":"Narayan","year":"2011","journal-title":"Appl Energy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1063\/1.1531823","article-title":"A review of symbolic analysis of experimental data","volume":"74","author":"Daw","year":"2003","journal-title":"Rev. Sci. Instrum."},{"key":"ref_22","first-page":"618","article-title":"Price graphs: Utilizing the structural information of financial time series for stock prediction","volume":"587","author":"Wu","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_23","first-page":"658","article-title":"Applications of symbolic dynamics in economic time series analysis","volume":"482","author":"Zhou","year":"2017","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_24","first-page":"108218","article-title":"Financial time series forecasting with multi-modality graph neural network","volume":"120","author":"Cheng","year":"2021","journal-title":"Pattern Recognit."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.procs.2024.03.022","article-title":"Modeling the Volatility of World Energy Commodity Prices Using the GARCH-Fractional Cointegration Model","volume":"234","author":"Izati","year":"2024","journal-title":"Procedia Comput. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Chen, L., Pan, L., and Zhang, K. (2024). The Dynamic Cointegration Relationship between International Crude Oil, Natural Gas, and Coal Price. Energies, 17.","DOI":"10.3390\/en17133126"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.eneco.2018.02.021","article-title":"A novel approach for oil price forecasting based on data fluctuation network","volume":"71","author":"Wang","year":"2018","journal-title":"Energy Econ."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Chen, H., Tian, L.X., Wang, M.G., and Zhen, Z.L. (2017). Analysis of the Dynamic Evolutionary Behavior of American Heating Oil Spot and Futures Price Fluctuation Networks. Sustainability, 9.","DOI":"10.3390\/su9040574"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"102077","DOI":"10.1016\/j.ribaf.2023.102077","article-title":"Estimating historical downside risks of global financial market indices via inflation rate-adjusted dependence graphs","volume":"65","author":"Choi","year":"2023","journal-title":"Res. Int. Bus. Financ."},{"key":"ref_30","first-page":"843","article-title":"Analysis on the topological properties of the linkage complex network between crude oil future price and spot price","volume":"60","author":"Gao","year":"2011","journal-title":"Acta Phys. Sin."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1016\/j.apenergy.2014.07.081","article-title":"Research on patterns in the fluctuation of the co-movement between crude oil futures and spot prices, A complex network approach","volume":"136","author":"An","year":"2014","journal-title":"Appl. Energy"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1016\/j.energy.2015.09.079","article-title":"Small and flat worlds: A complex network analysis of international trade in crude oil","volume":"93","author":"Yang","year":"2015","journal-title":"Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.apenergy.2014.06.064","article-title":"A dynamic analysis on global natural gas trade network","volume":"132","author":"Geng","year":"2014","journal-title":"Appl. Energy"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u201csmall-world\u201d networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.apenergy.2016.05.013","article-title":"Fluctuation behavior analysis of international crude oil and gasoline price based on complex network perspective","volume":"175","author":"Wang","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"35","DOI":"10.2307\/3033543","article-title":"A set of measures of centrality based on betweenness","volume":"40","author":"Freeman","year":"1977","journal-title":"Sociometry"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1080\/0022250X.2001.9990249","article-title":"A faster algorithm for betweenness centrality","volume":"25","author":"Brandes","year":"2001","journal-title":"J. Math. Sociol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4514","DOI":"10.7498\/aps.59.4514","article-title":"Dynamic analysis on the topological properties of the complex network of international oil prices","volume":"59","author":"Chen","year":"2010","journal-title":"Acta Phys. Sin."},{"key":"ref_39","first-page":"1496","article-title":"An Optimized Floyd Algorithm for the Shortest Path Problem","volume":"5","author":"Wei","year":"2010","journal-title":"J. Netw."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.socnet.2004.11.008","article-title":"Centrality and network flow","volume":"27","author":"Borgatti","year":"2005","journal-title":"Soc. Netw."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/821\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:39:56Z","timestamp":1760031596000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/821"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,25]]},"references-count":40,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["sym17060821"],"URL":"https:\/\/doi.org\/10.3390\/sym17060821","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,5,25]]}}}