Tens of thousands of parent companies control millions of subsidiaries through long chains ofintermediary entities in global corporate networks. Conversely, tens of millions of entities aredirectly held by sole owners. We propose an algorithm for identification of ultimate controllingentities in such networks that unifies direct and indirect control and allows for continuousinterpolation between the two concepts via a factor damping long paths. By exploiting onion-likeproperties of ownership networks the algorithm scales linearly with the network size and handlescircular ownership by design. We apply it to the universe of 4.2 mln UK companies and 4 mln oftheir holders to understand the distribution of control in the country. Furthermore, we providethe first independent evaluation of the control identification results. We reveal that the proposed{\alpha}-ICON algorithm identifies more than 96% of beneficiary entities from the evaluation set andsupersedes the existing approaches reported in the literature. We refer the superiority of{\alpha}-ICONalgorithm to its ability to correctly identify the parents long away from their subsidiaries in thenetwork.

中文翻译：

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洋葱状网络中的α-间接控制

数以万计的母公司通过全球企业网络中的长链中介实体控制数百万家子公司。相反，数以千万计的实体由唯一所有者直接持有。我们提出了一种用于识别此类网络中最终控制实体的算法，该算法统一了直接和间接控制，并允许通过阻尼长路径的因子在两个概念之间进行连续插值。通过利用所有权网络的洋葱状属性，该算法随网络规模线性扩展，并通过设计处理循环所有权。我们将其应用于 420 万家英国公司及其 400 万名持有人，以了解该国的控制权分布。此外，我们对控制识别结果进行了首次独立评估。我们揭示了所提出的{\alpha}-ICON 算法从评估集中识别了超过 96% 的受益实体，并取代了文献中报道的现有方法。我们将{\alpha}-ICONalgorithm 的优越性归结为它能够正确识别远离网络中的子公司的母公司。