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A Robust Method for Statistical Testing of Empirical Power-Law Distributions

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Algorithms and Models for the Web Graph (WAW 2020)

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The World-Wide-Web is a complex system naturally represented by a directed network of documents (nodes) connected through hyperlinks (edges). In this work, we focus on one of the most relevant topological properties that characterize the network, i.e. being scale-free. A directed network is scale-free if its in-degree and out-degree distributions have an approximate and asymptotic power-law behavior. If we consider the Web as a whole, it presents empirical evidence of such property. On the other hand, when we restrict the study of the degree distributions to specific sub-categories of websites, there is no longer strong evidence for it. For this reason, many works questioned the almost universal ubiquity of the scale-free property. Moreover, existing statistical methods to test whether an empirical degree distribution follows a power law suffer from large sample sizes and/or noisy data.

In this paper, we propose an extension of a state-of-the-art method that overcomes such problems by applying a Monte Carlo sub-sampling procedure on the graphs. We show on synthetic experiments that even small variations of true power-law distributed data causes the state-of-the-art method to reject the hypothesis, while the proposed method is more sound and stable under such variations.

Lastly, we perform a study on 3 websites showing that indeed, depending on their category, some accept and some refuse the hypothesis of being power-law. We argue that our method could be used to better characterize topological properties deriving from different generative principles: central or peripheral.

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Correspondence to Davide Garbarino .

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Garbarino, D., Tozzo, V., Vian, A., Barla, A. (2020). A Robust Method for Statistical Testing of Empirical Power-Law Distributions. In: Kamiński, B., Prałat, P., Szufel, P. (eds) Algorithms and Models for the Web Graph. WAW 2020. Lecture Notes in Computer Science(), vol 12091. Springer, Cham.

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