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Entropi ile Hiper Çizgelerde Merkezilik

Year 2021, Volume: 1 Issue: 2, 84 - 91, 31.12.2021

İhsan Tuğal , Zeydin Pala

Abstract

Entropi kompleks sistemlerde belirsizliği ölçmek için kullanılabilir. Hiper çizgeler gerçek dünyaya uygun verileri matematiksel olarak modellemek için yapı sunar. Bu çalışmada hiper çizge yapısındaki veriler üzerinde entropi kullanılarak analizler yapıldı. Düğüm derecesi ve hiper kenar derecesi kullanılarak düğümlerin ve hiper kenarların entropileri hesaplandı. Bu değerlere göre etkinlikleri bulundu. Ağırlıklı veya ağırlıksız ilişkisel yapılarda bu yöntemin uygulanabilirliği örnekler üzerinden gösterildi. Birden çok birimi ve çalışanı olan kurumlarda karar verme süreçlerinde destek amaçlı önerilen yöntemle elde edilen sonuçlar kullanılabilir.

Keywords

Entropi Hiper Çizgeler Karar Destek Sistemleri Merkezilik

References

  • Aggarwal, M. (2021). Attitude-based entropy function and applications in decision-making. Engineering Applications of Artificial Intelligence, 104, 104290. https://doi.org/10.1016/j.engappai.2021.104290
  • Aksoy, S. G., Joslyn, C., Ortiz Marrero, C., Praggastis, B., & Purvine, E. (2020). Hypernetwork science via high-order hypergraph walks. EPJ Data Science, 9(1), 16. https://doi.org/10.1140/epjds/s13688-020-00231-0
  • Bao, N., Cheng, N., Hernández-Cuenca, S., & Su, V. P. (2020). The quantum entropy cone of hypergraphs. SciPost Physics, 9(5), 067. https://doi.org/10.21468/SciPostPhys.9.5.067
  • Bloch, I., & Bretto, A. (2019). A New Entropy for Hypergraphs (pp. 143–154). https://doi.org/10.1007/978-3-030-14085-4_12
  • Boltzmann, L. (1964). Lectures on Gas Theory. Berkeley: University of California Press.
  • Bonacich, P., Cody Holdren, A., & Johnston, M. (2004). Hyper-edges and multidimensional centrality. Social Networks, 26(3), 189–203. https://doi.org/10.1016/j.socnet.2004.01.001
  • Borgatti, S. P., Everett, M. G., & Freeman, L. C. (2002). UCINET 6 For Windows: Software for Social Network Analysis, Analytic Technologies, Harvard, MA. Analytic Technologies.
  • Bromiley, P. A., Thacker, N. A., & Bouhova-Thacker, E. (2004). Shannon entropy, Renyi entropy, and information. Retrieved December 14, 2018, from http://www.tina-vision.net/docs/memos/2004-004.pdf
  • Chen, C., & Rajapakse, I. (2020). Tensor Entropy for Uniform Hypergraphs. IEEE Transactions on Network Science and Engineering, 7(4), 2889–2900. https://doi.org/10.1109/TNSE.2020.3002963
  • Deng, Y. (2016). Deng entropy. Chaos, Solitons and Fractals, 91, 549–553. https://doi.org/10.1016/j.chaos.2016.07.014
  • Hark, C., & Karcı, A. (2020). Karcı summarization: A simple and effective approach for automatic text summarization using Karcı entropy. Information Processing & Management, 57(3), 102187. https://doi.org/10.1016/j.ipm.2019.102187
  • Hu, D., Li, X. L., Liu, X. G., & Zhang, S. G. (2019). Extremality of Graph Entropy Based on Degrees of Uniform Hypergraphs with Few Edges. Acta Mathematica Sinica, English Series, 35(7), 1238–1250. https://doi.org/10.1007/s10114-019-8093-2
  • Karci, A. (2016). Fractional order entropy: New perspectives. Optik, 127(20), 9172–9177. https://doi.org/10.1016/j.ijleo.2016.06.119
  • Karcı, A. (2018). Notes on the published article “Fractional order entropy: New perspectives.” Optik - International Journal for Light and Electron Optics, 171, 107–108.
  • Klamt, S., Haus, U.-U., & Theis, F. (2009). Hypergraphs and Cellular Networks. PLoS Computational Biology, 5(5), e1000385. https://doi.org/10.1371/journal.pcbi.1000385
  • Martino, A., & Rizzi, A. (2020). (Hyper)graph Kernels over Simplicial Complexes. Entropy, 22(10), 1155. https://doi.org/10.3390/e22101155
  • Praggastis, B., Arendt, D., Joslyn, C., Purvine, E., Aksoy, S., & Monson, K. (2019). HyperNetX. Retrieved from https://github.com/pnnl/HyperNetX
  • Rényi, A. (1961). On measures of entropy and information. In Fourth Berkeley Symposium on Mathematical Statistics and Probability (p. 547). https://doi.org/10.1021/jp106846b
  • Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
  • Shannon, C. E. (1951). Prediction and Entropy of Printed English. Bell System Technical Journal, 30(1), 50–64. https://doi.org/10.1002/j.1538-7305.1951.tb01366.x
  • Shen, T., Zhang, Z., Chen, Z., Gu, D., Liang, S., Xu, Y., … Xie, X. (2018). A genome-scale metabolic network alignment method within a hypergraph-based framework using a rotational tensor-vector product. Scientific Reports, 8(1), 16376. https://doi.org/10.1038/s41598-018-34692-1
  • Sporns, O. (2018). Graph theory methods: applications in brain networks. Dialogues in Clinical Neuroscience, 20(2), 111–120. https://doi.org/10.31887/DCNS.2018.20.2/osporns
  • Sun, X., Yin, H., Liu, B., Chen, H., Cao, J., Shao, Y., & Viet Hung, N. Q. (2021). Heterogeneous Hypergraph Embedding for Graph Classification. In Proceedings of the 14th ACM International Conference on Web Search and Data Mining (pp. 725–733). New York, NY, USA: ACM. https://doi.org/10.1145/3437963.3441835
  • Tsallis, C. (2013). Entropy. In Computational Complexity: Theory, Techniques, and Applications (Vol. 9781461418, pp. 940–964). https://doi.org/10.1007/978-1-4614-1800-9_61
  • Tuğal, İ., & Karcı, A. (2019). Comparisons of Karcı and Shannon entropies and their effects on centrality of social networks. Physica A: Statistical Mechanics and Its Applications, 523, 352–363. https://doi.org/10.1016/j.physa.2019.02.026
  • Tuğal, İ., & Karcı, A. (2020). Determination of Influential Countries by Cultural and Geographical Parameters. Anemon Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi. https://doi.org/10.18506/anemon.563211
  • Tuğal, İ., Kaya, M., & Tuncer, T. (2013). Link prediction in disease and drug networks. In 6-th International Conference of Advanced Computer Systems and Networks: Design and Application (ACSN 2013) (pp. 46–50).
  • Wolf, M. M., Klinvex, A. M., & Dunlavy, D. M. (2016). Advantages to modeling relational data using hypergraphs versus graphs. In 2016 IEEE High Performance Extreme Computing Conference (HPEC) (pp. 1–7). IEEE. https://doi.org/10.1109/HPEC.2016.7761624

Centrality with Entropy in Hypergraphs

Year 2021, Volume: 1 Issue: 2, 84 - 91, 31.12.2021

İhsan Tuğal , Zeydin Pala

Abstract

Entropy is used to measure uncertainty in complex systems. Hypergraphs provide structure for mathematically modeling real-world data. In this study, analyzes were made using entropy on the data in the hypergraph structure. The entropies of the nodes and hyperedges were calculated using the node degree and hyper edge degree. Their activities were found according to these values. The applicability of this method in weighted or unweighted relational structures was demonstrated through examples. In institutions with multiple departments and employees, the results obtained with the proposed method can be used to support decision-making processes.

Keywords

Entropy Hypergraphs Decision Support Systems Centrality

References

  • Aggarwal, M. (2021). Attitude-based entropy function and applications in decision-making. Engineering Applications of Artificial Intelligence, 104, 104290. https://doi.org/10.1016/j.engappai.2021.104290
  • Aksoy, S. G., Joslyn, C., Ortiz Marrero, C., Praggastis, B., & Purvine, E. (2020). Hypernetwork science via high-order hypergraph walks. EPJ Data Science, 9(1), 16. https://doi.org/10.1140/epjds/s13688-020-00231-0
  • Bao, N., Cheng, N., Hernández-Cuenca, S., & Su, V. P. (2020). The quantum entropy cone of hypergraphs. SciPost Physics, 9(5), 067. https://doi.org/10.21468/SciPostPhys.9.5.067
  • Bloch, I., & Bretto, A. (2019). A New Entropy for Hypergraphs (pp. 143–154). https://doi.org/10.1007/978-3-030-14085-4_12
  • Boltzmann, L. (1964). Lectures on Gas Theory. Berkeley: University of California Press.
  • Bonacich, P., Cody Holdren, A., & Johnston, M. (2004). Hyper-edges and multidimensional centrality. Social Networks, 26(3), 189–203. https://doi.org/10.1016/j.socnet.2004.01.001
  • Borgatti, S. P., Everett, M. G., & Freeman, L. C. (2002). UCINET 6 For Windows: Software for Social Network Analysis, Analytic Technologies, Harvard, MA. Analytic Technologies.
  • Bromiley, P. A., Thacker, N. A., & Bouhova-Thacker, E. (2004). Shannon entropy, Renyi entropy, and information. Retrieved December 14, 2018, from http://www.tina-vision.net/docs/memos/2004-004.pdf
  • Chen, C., & Rajapakse, I. (2020). Tensor Entropy for Uniform Hypergraphs. IEEE Transactions on Network Science and Engineering, 7(4), 2889–2900. https://doi.org/10.1109/TNSE.2020.3002963
  • Deng, Y. (2016). Deng entropy. Chaos, Solitons and Fractals, 91, 549–553. https://doi.org/10.1016/j.chaos.2016.07.014
  • Hark, C., & Karcı, A. (2020). Karcı summarization: A simple and effective approach for automatic text summarization using Karcı entropy. Information Processing & Management, 57(3), 102187. https://doi.org/10.1016/j.ipm.2019.102187
  • Hu, D., Li, X. L., Liu, X. G., & Zhang, S. G. (2019). Extremality of Graph Entropy Based on Degrees of Uniform Hypergraphs with Few Edges. Acta Mathematica Sinica, English Series, 35(7), 1238–1250. https://doi.org/10.1007/s10114-019-8093-2
  • Karci, A. (2016). Fractional order entropy: New perspectives. Optik, 127(20), 9172–9177. https://doi.org/10.1016/j.ijleo.2016.06.119
  • Karcı, A. (2018). Notes on the published article “Fractional order entropy: New perspectives.” Optik - International Journal for Light and Electron Optics, 171, 107–108.
  • Klamt, S., Haus, U.-U., & Theis, F. (2009). Hypergraphs and Cellular Networks. PLoS Computational Biology, 5(5), e1000385. https://doi.org/10.1371/journal.pcbi.1000385
  • Martino, A., & Rizzi, A. (2020). (Hyper)graph Kernels over Simplicial Complexes. Entropy, 22(10), 1155. https://doi.org/10.3390/e22101155
  • Praggastis, B., Arendt, D., Joslyn, C., Purvine, E., Aksoy, S., & Monson, K. (2019). HyperNetX. Retrieved from https://github.com/pnnl/HyperNetX
  • Rényi, A. (1961). On measures of entropy and information. In Fourth Berkeley Symposium on Mathematical Statistics and Probability (p. 547). https://doi.org/10.1021/jp106846b
  • Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
  • Shannon, C. E. (1951). Prediction and Entropy of Printed English. Bell System Technical Journal, 30(1), 50–64. https://doi.org/10.1002/j.1538-7305.1951.tb01366.x
  • Shen, T., Zhang, Z., Chen, Z., Gu, D., Liang, S., Xu, Y., … Xie, X. (2018). A genome-scale metabolic network alignment method within a hypergraph-based framework using a rotational tensor-vector product. Scientific Reports, 8(1), 16376. https://doi.org/10.1038/s41598-018-34692-1
  • Sporns, O. (2018). Graph theory methods: applications in brain networks. Dialogues in Clinical Neuroscience, 20(2), 111–120. https://doi.org/10.31887/DCNS.2018.20.2/osporns
  • Sun, X., Yin, H., Liu, B., Chen, H., Cao, J., Shao, Y., & Viet Hung, N. Q. (2021). Heterogeneous Hypergraph Embedding for Graph Classification. In Proceedings of the 14th ACM International Conference on Web Search and Data Mining (pp. 725–733). New York, NY, USA: ACM. https://doi.org/10.1145/3437963.3441835
  • Tsallis, C. (2013). Entropy. In Computational Complexity: Theory, Techniques, and Applications (Vol. 9781461418, pp. 940–964). https://doi.org/10.1007/978-1-4614-1800-9_61
  • Tuğal, İ., & Karcı, A. (2019). Comparisons of Karcı and Shannon entropies and their effects on centrality of social networks. Physica A: Statistical Mechanics and Its Applications, 523, 352–363. https://doi.org/10.1016/j.physa.2019.02.026
  • Tuğal, İ., & Karcı, A. (2020). Determination of Influential Countries by Cultural and Geographical Parameters. Anemon Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi. https://doi.org/10.18506/anemon.563211
  • Tuğal, İ., Kaya, M., & Tuncer, T. (2013). Link prediction in disease and drug networks. In 6-th International Conference of Advanced Computer Systems and Networks: Design and Application (ACSN 2013) (pp. 46–50).
  • Wolf, M. M., Klinvex, A. M., & Dunlavy, D. M. (2016). Advantages to modeling relational data using hypergraphs versus graphs. In 2016 IEEE High Performance Extreme Computing Conference (HPEC) (pp. 1–7). IEEE. https://doi.org/10.1109/HPEC.2016.7761624
There are 28 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

İhsan Tuğal 0000-0003-1898-9438

Zeydin Pala 0000-0002-2642-7788

Publication Date December 31, 2021
Submission Date December 8, 2021
Published in Issue Year 2021 Volume: 1 Issue: 2

Cite

APA Tuğal, İ., & Pala, Z. (2021). Centrality with Entropy in Hypergraphs. Rahva Journal of Technical and Social Studies, 1(2), 84-91.
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