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Determining the best algorithm to detect community structures in networks: application to power systems

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Abstract

A common feature of many networks is the presence of communities, or groups of relatively densely connected nodes with sparse connections between groups. An understanding of community structures could enable the network design for improved system performance. For electric power systems, most work in the detection of community structures (i) selects a specific algorithm to perform the detection of communities (or compares a proposed algorithm against algorithms), and (ii) focuses on topological information about the networks. The objective of this article is to provide a framework to improve the selection of appropriate community detection algorithms for a family of networks with similar structures. We propose an approach to determine the most effective community detection algorithm for a set of networks and compare which algorithms provide the most similar partitions across these networks. To illustrate the comparison of various community detection algorithms, 16 electric power systems are analyzed.

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References

  • Aldecoa R (2012) Detección de comunidades en redes complejas. MS tesis, Universidad Politécnica de Valencia, Valencia, Spain

  • Almoghathawi Y, Barker K (2020) Restoring community structures in interdependent infrastructure networks. IEEE Trans Netw Sci Eng 7(3):1355–1367

    Article  Google Scholar 

  • Amelio A, Pizzuti C (2015) Is normalized mutual information a fair measure for comparing community detection methods? In: ASONAM '15: proceedings of the 2015 IEEE/ACM international conference on advances in social networks analysis and mining, pp 1584–1585

  • Blondel V, Guillaume J, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech: Theory Exp 10:10008

    Article  Google Scholar 

  • Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: structure and nynamics. Phys Rep 424:175–308

    Article  Google Scholar 

  • Borges L, Nunes P, Marques V, Bernardino J (2013) Comparison of data mining techniques and tools for data classification. In: C3S2E '13: proceedings of the international conference on computer science and software engineering, pp 113–116

  • Chakraborty T, Srinivasan S, Ganguly N, Mukherjee A, Bhowmick S (2014) On the permanence of vertices in network communities. In: C3S2E '13: proceedings of the international conference on computer science and software engineering, pp 113–116

  • Chen Z, Xie Z, Zhang Q (2015) Community detection based on local topological information and its application in power grid. Neurocomputing 170:384–392

    Article  Google Scholar 

  • Clauset A, Newman ME, Moore C (2004) Finding community structure in very large networks. Phys Rev E 70(6):066111

    Article  CAS  Google Scholar 

  • Coello C, Van Veldhuizen D, Lamont G (2002) Evolutionary algorithms for solving multi-objective problems. Kluwer Academic Publishers, New York

    Book  Google Scholar 

  • Crucitti P, Latora V, Marchiori M (2004) A topological analysis of the italian electric power grid. Physica A 338:92–97

    Article  Google Scholar 

  • Csárdi G, Nepusz T (2006) The igraph software package for complex network research. InterJournal, Complex Systems, 1695

  • Domgue FG, Tsopze N, Ndoundam R (2020) Community structure extraction in directed network using triads. Int J Gen Syst 49(8):819–842

    Article  Google Scholar 

  • Du N, Wang B, Wu B (2008) Community detection in complex networks. J Comput Sci Technol 23(4):672–683

    Article  Google Scholar 

  • Dylewsky D, Yang X, Tartakovsky A, Kutz JN (2019) Engineering structural robustness in power grid networks susceptible to community desynchronization. Appl Netw Sci 4:24

    Article  Google Scholar 

  • Floyd MK, Barker K, Rocco CM, Whitman MG (2017) A multi-criteria decision analysis technique for stochastic task criticality in project management. Eng Manage J 29(3):165–178

    Article  Google Scholar 

  • Fortunato S (2010) Community detection in graphs. Phys Rep 486:75–174

    Article  Google Scholar 

  • Gfeller D, Chappelier JC, de Los Rios P (2005) Finding instabilities in the community structure of complex networks. Phys Rev E 72:056135

    Article  CAS  Google Scholar 

  • Girvan M, Newman ME (2002) Community structure in social and biological networks. Proc Natl Acad Sci 99:7821–7826

    Article  CAS  Google Scholar 

  • Greco S, Ehrgott M, Figueira JR (2016) Multiple criteria decision analysis: state of the art surveys. Springer, New York

    Book  Google Scholar 

  • Guerrero M, Montoya FG, Baños R, Alcayde A, Gil C (2018) Community detection in national-scale high voltage transmission networks using genetic algorithms. Adv Eng Inform 38:232–241

    Article  Google Scholar 

  • Guerrero M, Baños R, Gil C, Montoya FG, Alcayde A (2019) Evolutionary algorithms for community detection in continental-scale high-voltage transmission grids. Symmetry 11:1472

    Article  Google Scholar 

  • Häring I, Fehling-Kaschek M, Miller N et al (2021) A performance-based tabular approach for joint systematic improvement of risk control and resilience applied to telecommunication grid, gas network, and ultrasound localization system. Environ Syst Decis. https://doi.org/10.1007/s10669-021-09811-5

    Article  Google Scholar 

  • Holmgren AJ (2006) Using graph models to analyze the vulnerability of electric power networks. Risk Anal 26(4):955–969

    Article  Google Scholar 

  • Hu Y, Ding Y, Fan Y, Di Z (2010) Measuring significance of community structure in complex networks. Phys Rev E 82(6):066106

    Article  CAS  Google Scholar 

  • Hubert L, Arabie P (1985) Comparing partitions. J Classif 2(1):193–218

    Article  Google Scholar 

  • Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, New York

    Book  Google Scholar 

  • Jamei M, Scaglione A, Peisert S (2018) Low-resolution fault localization using phasor measurement units with community detection. In: 2018 IEEE international conference on communications, control, and computing technologies for smart grids (SmartGridComm), pp 1–6

  • Karrer B, Levina E, Newman MEJ (2008) Robustness of community structure in networks. Phys Rev E 77(4):046119

    Article  CAS  Google Scholar 

  • Kim H, Olave-Rojas D, Álvarez-Miranda E, Son S-W (2018) In-depth data on the network structure and hourly activity of the central Chilean power grid. Sci Data 5:180209

    Article  Google Scholar 

  • Labatut V (2015) Generalized measures for the evaluation of community detection methods. Int J Soc Netw Anal Min 2(1):44–63

    Article  Google Scholar 

  • Li J, Dueñas-Osorio L, Chen C, Shi C (2017) AC power flow importance measures considering multi-element failures. Reliab Eng Syst Saf 160:89–97

    Article  Google Scholar 

  • Linkov I, Eisenberg DA, Plourde K et al (2013) Resilience metrics for cyber systems. Environ Syst Decis 33:471–476

    Article  Google Scholar 

  • Makridakis S, Hibon M (2000) The M3-competition: results, conclusions and implications. Int J Forecast 16(4):451–476

    Article  Google Scholar 

  • Mei S, Zhang X, Cao M (2011) Power grid complexity. Springer, Heidelberg

  • Meila M (2003) Comparing clusterings by the variation of information. Learning theory and kernel machines. Springer, Berlin, pp 173–187

    Chapter  Google Scholar 

  • Moghavvemi M, Faruque MO (1999) Power system security and voltage collapse: A line outage based indicator for prediction. Int J Electr Power Energy Syst 21(6):455–461

  • Mosalman YM (2015) TOPSIS R package. https://cran.r-project.org/web/packages/topsis/index.html. Accessed 11 Oct 2021

  • Newman ME (2006a) Modularity and community structure in networks. Proc Natl Acad Sci 103:8577–8582

    Article  CAS  Google Scholar 

  • Newman ME (2006b) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74(3):036104

    Article  CAS  Google Scholar 

  • Newman ME, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69(2):026113

    Article  CAS  Google Scholar 

  • Pagani GA, Aiello M (2013) The power grid as a complex network: a survey. Physica A 392:2688–2700

    Article  Google Scholar 

  • Pahwa S, Youssef M, Schumm P, Scoglio C, Schulz N (2013) Optimal intentional islanding to enhance the robustness of power grid networks. Physica A 392:3741–3754

    Article  Google Scholar 

  • Pihur V, Datta S, Datta S (2020) RankAggreg, an R package for weighted rank aggregation. https://cran.r-project.org/web/packages/RankAggreg/vignettes/RankAggreg.pdf. Accessed 11 Oct 2021

  • Pons P, Latapy M (2005) Computing communities in large networks using random walks. Computer and information sciences-ISCIS. Springer, Berlin, pp 284–293

    Google Scholar 

  • Porter MA, Onnela J-P, Mucha PJ (2009) Communities in networks. Not Am Math Soc 56(9):1082–1097

    Google Scholar 

  • R Core Team (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing. http://www.R-project.org/. Accessed 11 Oct 2021

  • Raghavan U, Albert R, Kumara S (2007) Near linear time algorithm to detect community structures in large-scale networks. Phys Rev E 76(3):036106

    Article  CAS  Google Scholar 

  • Ramirez-Marquez JE, Rocco CM, Barker K, Moronta J (2018) Quantifying the resilience of community structures in networks. Reliab Eng Syst Saf 169:466–474

    Article  Google Scholar 

  • Rand WM (1971) Objective criteria for the evaluation of clustering methods. J Am Stat Assoc 66(336):846–850

    Article  Google Scholar 

  • Reichardt J, Bornoldt S (2006) Statistical mechanics of community detection. Phys Rev E 74(1):016110

    Article  CAS  Google Scholar 

  • Rocco C (2008) Análisis del sistema eléctrico venezolano desde la perspectiva de la teoría de redes complejas. Revista De La Facultad De Ingeniería Universidad Central De Venezuela 23(1):103–109

    Google Scholar 

  • Rocco C, Ramirez-Marquez J (2011) Vulnerability metrics and analysis for communities in complex networks. Reliab Eng Syst Saf 96:1360–1366

    Article  Google Scholar 

  • Rocco CM, Ramirez-Marquez JE, Moronta J, Gama D (2016a) Robustness in network community detection under links weights uncertainties. Reliab Eng Syst Saf 153:88–95

    Article  Google Scholar 

  • Rocco CM, Hernandez E, Barker K (2016b) A multicriteria decision analysis technique for stochastic ranking, with application to network resilience. Risk Uncertain Eng Syst 2(1):04015018

    Article  Google Scholar 

  • Rocco CM, Barker K, Hernandez-Perdomo E (2016c) Stochastic ranking of alternatives with ordered weighted averaging: comparing network recovery strategies. Syst Eng 19(5):436–447

    Article  Google Scholar 

  • Rosato V, Bologna S, Tiriticco F (2007) Topological properties of high-voltage electric transmission networks. Electr Power Syst Res 77:99–105

    Article  Google Scholar 

  • Rosato V, Issacharoff L, Bologna S (2009) Influence of the topology on the power flux of the Italian high-voltage electric network. http://arxiv.org/abs/0909.1664

  • Rossi RA, Ahmed NK (2015) The network data repository with interactive graph analytics and visualization. http://networkrepository.com. Accessed 11 Oct 2021

  • Rosvall M, Bergstrom C (2008) Maps of information flow reveal community structure in complex networks. Proc Natl Acad Sci 105(4):1118–1123

    Article  CAS  Google Scholar 

  • Sampaio RA, Oliveira GC, da Costa Jr LC, Garcia JD (2019) Community detection for power systems network aggregation considering renewable variability. https://arxiv.org/abs/1911.04279

  • Sánchez-García RJ, Fennelly M, Norris S, Wright N, Niblo G, Brodzki J, Bialek JW (2014) Hierarchical spectral clustering of power grids. IEEE Trans Power Syst 29(5):2229–2237

    Article  Google Scholar 

  • Schaub M, Delvenne J, Yaliraki S, Barahona M (2012) Markov dynamics as a zooming lens for multiscale community detection: non clique-like communities and the field-of-view limit. PLoS ONE 7(2):e32210

    Article  CAS  Google Scholar 

  • Tarsitano A (2009) Comparing the effectiveness of rank correlation statistics, working papers 200906, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania.” https://ideas.repec.org/p/clb/wpaper/200906.html. Accessed 11 Oct 2021

  • Yajure C, Montilla D, Ramirez-Marquez JE, Rocco CM (2013) Network vulnerability assessment via bi-objective optimization with a fragmentation approach as proxy. J Risk Reliab 227(6):576–585

    Google Scholar 

  • Yang Z, Algesheimer R, Tessone CJ (2016) A comparative analysis of community detection algorithms on artificial networks. Sci Rep 6:30750

    Article  CAS  Google Scholar 

  • Zhao C, Zhao J, Wu C, Wang X, Xue F, Lu S (2019) Power grid partitioning based on functional community structure. IEEE Access 7:152624–152634

    Article  Google Scholar 

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Acknowledgements

This work was partially supported by the National Science Foundation through award 1635813.

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Authors and Affiliations

  1. Facultad de Ingeniería, Universidad Central de Venezuela, Caracas, Venezuela

    Claudio M. Rocco

  2. School of Industrial and Systems Engineering, University of Oklahoma, 202 W. Boyd St., Rm. 124, Norman, OK, 73019, USA

    Kash Barker

  3. Departamento de Tecnología Industrial, Universidad Simón Bolívar, Caracas, Venezuela

    Jose Moronta

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  1. Claudio M. Rocco
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Correspondence to Kash Barker.

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This work was supported in part by the National Science Foundation, Division of Civil, Mechanical, and Manufacturing Innovation, under award 1635813.

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Rocco, C.M., Barker, K. & Moronta, J. Determining the best algorithm to detect community structures in networks: application to power systems. Environ Syst Decis 42, 251–264 (2022). https://doi.org/10.1007/s10669-021-09833-z

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