Abstract
Real-world complex systems can be modeled as homogeneous or heterogeneous graphs composed by nodes connected by edges. The importance of nodes and edges is formally described by a set of measures called centralities which are typically studied for graphs of small size. The proliferation of digital collection of data has led to huge graphs with billions of nodes and edges. For this reason, we focus on two new algorithms, Game of Thieves and WERW-Kpath which are computationally-light alternatives to the canonical centrality measures such as degree, node and edge betweenness, closeness and clustering. We explore the correlation among these measures using the Spearman’s correlation coefficient on real criminal networks extracted from judicial documents of three Mafia operations. Results of our analysis indicate that Game of Thieves could be used as a more economic replacement to rank both nodes and edges and WERW-Kpath to rank edges.
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Notes
- 1.
- 2.
Available in Python 2 at: http://github.com/dcmocanu/centrality-metrics-complex-networks
- 3.
Available in Java at: http://www.emilio.ferrara.name/code/werw-kpath/
References
Agreste, S., Catanese, S., De Meo, P., Ferrara, E., Fiumara, G.: Network structure and resilience of Mafia syndicates. Inf. Sci. 351, 30–47 (2016). https://doi.org/10.1016/j.ins.2016.02.027
Berlusconi, G., Calderoni, F., Parolini, N., Verani, M., Piccardi, C.: Link prediction in criminal networks: a tool for criminal intelligence analysis. PLOS ONE 11(4), 1–21 (2016). https://doi.org/10.1371/journal.pone.0154244
Borgatti, S.P., Everett, M.G., Freeman, L.C.: UCINET for Windows: Software for Social Network Analysis. Analytic Technologies, Harvard, MA (2002)
Brandes, U.: On variants of shortest-path betweenness centrality and their generic computation. Soc. Netw. 30(2), 136–145 (2008). https://doi.org/10.1016/j.socnet.2007.11.001
Bröhl, T., Lehnertz, K.: Centrality-based identification of important edges in complex networks. Chaos Interdiscipl. J. Nonlinear Sci. 29(3), 033115 (2019). https://doi.org/10.1063/1.5081098
Calderoni, F.: Identifying mafia bosses from meeting attendance. In: Masys, A.J. (ed.) Networks and Network Analysis for Defence and Security, pp. 27–48. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04147-6_2
Calderoni, F.: Predicting organized crime leaders. In: Bichler, G., Malm, A. (eds.) Disrupting Criminal Networks: Network Analysis in Crime Prevention, pp. 89–110. Lynne Rienner Publishers, Boulder (2015). http://hdl.handle.net/10807/68084
Calderoni, F., Brunetto, D., Piccardi, C.: Communities in criminal networks: a case study. Soc. Netw. 48, 116–125 (2017). https://doi.org/10.1016/j.socnet.2016.08.003
Calderoni, F., Catanese, S., De Meo, P., Ficara, A., Fiumara, G.: Robust link prediction in criminal networks: a case study of the Sicilian Mafia. Expert Syst. Appl. 161, 113666 (2020). https://doi.org/10.1016/j.eswa.2020.113666
Cavallaro, L., et al.: Criminal Network: The Sicilian Mafia. “Montagna Operation”, July 2020. https://doi.org/10.5281/zenodo.3938818
Cavallaro, L., et al.: Disrupting resilient criminal networks through data analysis: the case of Sicilian Mafia. PLoS ONE 15(8), 1–22 (2020). https://doi.org/10.1371/journal.pone.0236476
Cavallaro, L., et al.: Graph comparison and artificial models for simulating real criminal networks. In: Benito, R., Cherifi, C., Cherifi, H., Moro, E., Rocha, L., Sales-Pardo, M. (eds.) Complex Networks and Their Applications IX. COMPLEX NETWORKS 2020. Studies in Computational Intelligence, vol. 944, pp. 286–297. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-65351-4_23
Chen, P., Popovich, P.: Correlation: Parametric and Nonparametric Measures. Sage University Papers Series, no. 07–139, Sage Publications, Thousand Oaks (2002)
Crossley, N.: Social Network Analysis (chap. 6), pp. 87–103. Wiley, Hoboken (2019). https://doi.org/10.1002/9781119429333.ch6
De Meo, P., Ferrara, E., Fiumara, G., Provetti, A.: Enhancing community detection using a network weighting strategy. Inf. Sci. 222, 648–668 (2013). https://doi.org/10.1016/j.ins.2012.08.001
De Meo, P., Ferrara, E., Fiumara, G., Provetti, A.: Mixing local and global information for community detection in large networks. J. Comput. Syst. Sci. 80(1), 72–87 (2014). https://doi.org/10.1016/j.jcss.2013.03.012
De Meo, P., Ferrara, E., Fiumara, G., Ricciardello, A.: A novel measure of edge centrality in social networks. Knowl. Based Syst. 30, 136–150 (2012). https://doi.org/10.1016/j.knosys.2012.01.007
Duijn, P.A.C., Kashirin, V., Sloot, P.M.A.: The relative ineffectiveness of criminal network disruption. Sci. Rep. 4(1), 4238 (2014). https://doi.org/10.1038/srep04238
Ferrara, E., De Meo, P., Catanese, S., Fiumara, G.: Detecting criminal organizations in mobile phone networks. Expert Syst. Appl. 41(13), 5733–5750 (2014). https://doi.org/10.1016/j.eswa.2014.03.024
Ferrara, E., De Meo, P., Catanese, S., Fiumara, G.: Visualizing criminal networks reconstructed from mobile phone records. In: CEUR Workshop Proceedings, vol. 1210 (2014)
Ficara, A., et al.: Criminal networks analysis in missing data scenarios through graph distances (2021)
Ficara, A., et al.: Social network analysis of Sicilian Mafia interconnections. In: Cherifi, H., Gaito, S., Mendes, J.F., Moro, E., Rocha, L.M. (eds.) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol. 882, pp. 440–450. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-36683-4_36
Ficara, A., Fiumara, G., De Meo, P., Liotta, A.: Correlations among game of thieves and other centrality measures in complex networks. In: Fortino, G., Liotta, A., Gravina, R., Longheu, A. (eds.) Data Science and Internet of Things. Internet of Things, pp. 43–62. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-67197-6_3
Ficara, A., Fiumara, G., De Meo, P., Catanese, S.: Multilayer network analysis: the identification of key actors in a Sicilian Mafia operation. In: Perakovic, D., Knapcikova, L. (eds.) Future Access Enablers for Ubiquitous and Intelligent Infrastructures. FABULOUS 2021. LNICS, SITE, vol. 382, pp. 120–134. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-78459-1_9
Ficara, A., Fiumara, G., De Meo, P., Liotta, A.: Correlation analysis of node and edge centrality measures in artificial complex networks. In: Yang, X.-S., Sherratt, S., Dey, N., Joshi, A. (eds.) Proceedings of Sixth International Congress on Information and Communication Technology. LNNS 216, vol. 3. Springer, Cham (2021). https://doi.org/10.1007/978-981-16-1781-2_78
Freeman, L.C.: Centrality in social networks conceptual clarification. Soc. Netw. 1(3), 215–239 (1978). https://doi.org/10.1016/0378-8733(78)90021-7
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002). https://doi.org/10.1073/pnas.122653799
Grassi, R., Calderoni, F., Bianchi, M., Torriero, A.: Betweenness to assess leaders in criminal networks: new evidence using the dual projection approach. Soc. Netw. 56, 23–32 (2019). https://doi.org/10.1016/j.socnet.2018.08.001
Hagberg, A.A., Schult, D.A., Swart, P.J.: Exploring network structure, dynamics, and function using NetworkX. In: Varoquaux, G., Vaught, T., Millman, J. (eds.) Proceedings of the 7th Python in Science Conference, Pasadena, CA USA, pp. 11–15 (2008)
Kang, U., Papadimitriou, S., Sun, J., Tong, H.: Centralities in large networks: algorithms and observations. In: Proceedings of the 11th SIAM International Conference on Data Mining, SDM 2011, pp. 119–130 (2011). https://doi.org/10.1137/1.9781611972818.11
Kendall, M., Gibbons, J.: Rank Correlation Methods. Charles Griffin Book, E. Arnold (1990)
von Lampe, K., Johansen, P.O.: Organized crime and trust: on the conceptualization and empirical relevance of trust in the context of criminal networks. Glob. Crime 6(2), 159–184 (2004). https://doi.org/10.1080/17440570500096734
Mastrobuoni, G., Patacchini, E.: Organized crime networks: an application of network analysis techniques to the American Mafia. Rev. Netw. Econ. 11(3) (2012). https://doi.org/10.1515/1446-9022.1324
Meghanathan, N., Yang, F.: Correlation analysis: edge betweenness centrality vs. neighbourhood overlap. Int. J. Netw. Sci. 1(4), 299–324 (2019). https://doi.org/10.1504/IJNS.2019.102284
Mocanu, D.C., Exarchakos, G., Liotta, A.: Decentralized dynamic understanding of hidden relations in complex networks. Sci. Rep. 8(1), 1571 (2018). https://doi.org/10.1038/s41598-018-19356-4
Paoli, L.: Italian organised crime: mafia associations and criminal enterprises. Glob. Crime Today Chang. Face Org. Crime 6(1), 19–31 (2004). https://doi.org/10.1080/1744057042000297954
Paoli, L.: Mafia Brotherhoods: Organized Crime, Italian style. Oxford University Press, Oxford Scholarship Online (2008). https://doi.org/10.1093/acprof:oso/9780195157246.001.0001
Piccardi, C., Berlusconi, G., Calderoni, F., Parolini, N., Verani, M.: Oversize network (2016). https://doi.org/10.6084/m9.figshare.3156067.v1
Rajeh, S., Savonnet, M., Leclercq, E., Cherifi, H.: Investigating centrality measures in social networks with community structure. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds.) Complex Networks and Their Applications IX. COMPLEX NETWORKS 2020. Studies in Computational Intelligence, vol. 943, pp. 211–222. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-65347-7_18
Ratner, B.: The correlation coefficient: its values range between +1/\(-1\), or do they? J. Target. Meas. Anal. Mark. 17(2), 139–142 (2009). https://doi.org/10.1057/jt.2009.5
Ronqui, J.R.F., Travieso, G.: Analyzing complex networks through correlations in centrality measurements. J. Stat. Mech. Theory Exp. 2015(5), P05030 (2015). https://doi.org/10.1088/1742-5468/2015/05/p05030
Saramäki, J., Kivelä, M., Onnela, J.P., Kaski, K., Kertész, J.: Generalizations of the clustering coefficient to weighted complex networks. Phys. Rev. E 75(2), 027105 (2007). https://doi.org/10.1103/PhysRevE.75.027105
Shao, C., Cui, P., Xun, P., Peng, Y., Jiang, X.: Rank correlation between centrality metrics in complex networks: an empirical study. Open Phys. 16(1), 1009–1023 (2018). https://doi.org/10.1515/phys-2018-0122
Spearman, C.: General intelligence, objectively determined and measured. Am. J. Psychol. 15(2), 201–292 (1904). https://doi.org/10.2307/1412107
van Steen, M.: Graph Theory and Complex Networks: An Introduction. Maarten van Steen (2010)
Valente, T.W., Coronges, K., Lakon, C., Costenbader, E.: How correlated are network centrality measures? Connections (Toronto, Ont.) 28(1), 16–26 (2008)
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Ficara, A., Saitta, R., Fiumara, G., De Meo, P., Liotta, A. (2021). Game of Thieves and WERW-Kpath: Two Novel Measures of Node and Edge Centrality for Mafia Networks. In: Teixeira, A.S., Pacheco, D., Oliveira, M., Barbosa, H., Gonçalves, B., Menezes, R. (eds) Complex Networks XII. CompleNet-Live 2021. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-81854-8_2
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