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Segregation discovery in a social network of companies

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Abstract

We introduce a framework for the data-driven analysis of social segregation of minority groups, and challenge it on a complex scenario. The framework builds on quantitative measures of segregation, called segregation indexes, proposed in the social science literature. The segregation discovery problem is introduced, which consists of searching sub-groups of population and minorities for which a segregation index is above a minimum threshold. A search algorithm is devised that solves the segregation problem by computing a multi-dimensional data cube that can be explored by the analyst. The machinery underlying the search algorithm relies on frequent itemset mining concepts and tools. The framework is challenged on a cases study in the context of company networks. We analyse segregation on the grounds of sex and age for directors in the boards of the Italian companies. The network includes 2.15M companies and 3.63M directors.

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Notes

  1. The geometric interpretation of the Gini index is provided in the space [0, 1] × [0, 1]. The Lorenz curve plots the cumulative fraction of minority against the cumulative fraction of majority. Formally, assume that p 1,…,p n are in descending order. The Lorenz curve f() is the piece-wise linear function such that f(0) = 0, f(1) = 1, and, for i ∈ [1,n], \(f(\hat {X}_{i}) = \hat {Y}_{i}\) where \(\hat {X}_{i}\) is the cumulative fraction of the minority group up to unit i, and \(\hat {Y}_{i}\) is the cumulative fraction of the majority group up to unit i. The diagonal represents the perfect equality of distribution of majority vs minority population. The Gini index is twice the area between the Lorenz curve and the diagonal. See (Duncan and Duncan 1955; Xu 2003) for details.

  2. Level 3 of the Nomenclature of Territorial Units for Statistics (NUTS)(International Organization for Standardization 2013).

  3. We adopted the methods and software from (Alstott et al. 2014) for fitting heavily tailed distributions. The distribution with the best loglikelihood ratio is selected among power laws, truncated power laws, exponentials, stretched exponentials, and log-normals.

  4. See also https://en.wikipedia.org/wiki/Gender_representation_on_corporate_boards_of_directors.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy

    Alessandro Baroni & Salvatore Ruggieri

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  1. Alessandro Baroni
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  2. Salvatore Ruggieri
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Correspondence to Alessandro Baroni.

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A preliminary version of the results of this paper appeared in (Baroni and Ruggieri 2015).

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Baroni, A., Ruggieri, S. Segregation discovery in a social network of companies. J Intell Inf Syst 51, 71–96 (2018). https://doi.org/10.1007/s10844-017-0485-0

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