Stefania Vitali; James B. Glattfelder; Stefano Battiston

“ Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie) . ”

“ Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. ”

“ This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.
Introduction
A common intuition among scholars and in the media sees the global economy as being dominated by a handful of powerful transnational corporations (TNCs) . However, this has not been confirmed or rejected with explicit numbers. A quantitative investigation is not a trivial task because firms may exert control over other firms via a web of direct and indirect ownership relations which extends over many countries. ”

“ In any case, it is remarkable that our results on concentration are robust with respect to three very different models used to infer control from ownership. The second issue concerns the control that financial institutions effectively exert. According to some theoretical arguments, in general, financial institutions do not invest in equity shares in order to exert control. ”

“ However, a necessary precondition to such investigations is to uncover the worldwide structure of corporate control. This was never performed before and it is the aim of the present work.
Methods Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. ”

“ As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.
Network topology. (A) A bow-tie consists of in-section (IN) , out-section (OUT) , strongly connected component or core (SCC) , and tubes and tendrils (T&T) . (B) Bow-tie structure of the largest connected component (LCC) and other connected components (OCC) . Each section volume scales logarithmically with the share of its TNCs operating revenue. ”

“ References 1 2 Barabási, A & Albert, R, “Emergence of scaling in random networks.”, Science 286: 509, pmid:10521342 ↑ Schweitzer, F; Fagiolo, G; Sornette, D; Vega-Redondo, F & Vespignani, A, “Economic networks: The new challenges.”, Science 325: 422–425, pmid:19628858 1 2 Fagiolo, G ”