Abstract
Benford’s law, also known as the law of the first digits, shows that the first digits of numbers in a series of records from various sources are not uniformly distributed, but follow a decreasing order of occurrence from “1” to “9”. It is commonly used to detect anomalies in data series and can also raise suspicions of fraud. In this paper, the applicability of Benford’s law to different types of networks is studied. The study analyses ten real networks of different sizes and three theoretical network models, examining the degree centrality, the betweenness centrality and the closeness centrality distributions of each network. The results indicate that only the betweenness centrality distributions of real networks follow Benford's law. The study suggests that differences in significant number distributions may be due to internal properties of networks, requiring further analysis to identify necessary and sufficient conditions and assumptions for applying Benford’s law. Overall, the study highlights the potential of using Benford’s law in network analysis to identify properties and potential anomalies in real-world applications.
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References
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999). https://doi.org/10.1126/science.286.5439.509
Geyer, C.L., Williamson, P.P.: Detecting fraud in data sets using benford’s law. Commun. Stat. – Simul. Comput. 33, 229–246 (2004)
Gilbert, E.N.: Random graphs. Ann. Math. Stat. 30(4), 1141–1144 (1959). https://doi.org/10.1214/aoms/1177706098
Golbeck, J.: Benford’s law applies to online social networks. PLoS ONE 10(8), e0135169 (2015). https://doi.org/10.1371/journal.pone.0135169
Iorliam, A.: Natural laws (Benford’s law and Zipf’s Law) for network traffic analysis. In: Cybersecurity in Nigeria. SC, pp. 3–22. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-15210-9_2
Morzy, M., Kajdanowicz, T., Szymański, B.K.: Benford’s distribution in complex networks. Sci. Rep. (2016). https://doi.org/10.1038/srep34917
Nigrini, M.J.: ‘I’ve got your number. J. Accountancy 187(5), 79 (1999). https://www.journalofaccountancy.com/issues/1999/may/nigrini.html
Schütz, F.: Des statisticiens traquent la fraude électrorale, Le Temps (2013). https://www.letemps.ch/sciences/statisticiens-traquent-fraude-electorale
Tichenor, C., Davis, B.: The applicability of Benford’s Law to the buying behavior of foreign military sales customers. Global J. Bus. Res. 2(2), 77–85 (2008). https://ssrn.com/abstract=1543525
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998). https://doi.org/10.1038/30918
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Maldonado, A., Pereda, M., Ortega-Mier, M. (2024). Exploring the Applicability of Benford's Law in Network Science and Graph Theory. In: Bautista-Valhondo, J., Mateo-Doll, M., Lusa, A., Pastor-Moreno, R. (eds) Proceedings of the 17th International Conference on Industrial Engineering and Industrial Management (ICIEIM) – XXVII Congreso de Ingeniería de Organización (CIO2023). CIO 2023. Lecture Notes on Data Engineering and Communications Technologies, vol 206. Springer, Cham. https://doi.org/10.1007/978-3-031-57996-7_2
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DOI: https://doi.org/10.1007/978-3-031-57996-7_2
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