Exploring the Applicability of Benford's Law in Network Science and Graph Theory

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.