The layered structure of company share networks

Abstract

We present a framework for the analysis of corporate governance problems using network science and graph algorithms on ownership networks. In such networks, nodes model companies/shareholders and edges model shares owned. Inspired by the widespread pyramidal organization of corporate groups of companies, we model ownership networks as layered graphs, and exploit the layered structure to design feasible and efficient solutions to three key problems of corporate governance. The first one is the long-standing problem of computing direct and indirect ownership (integrated ownership problem). The other two problems are introduced here: computing direct and indirect dividends (dividend problem), and computing the group of companies controlled by a parent shareholder (corporate group problem). We conduct an extensive empirical analysis of the Italian ownership network, which, with its 3.9M nodes, is 30× the largest network studied so far.

Corporate payments networks and credit risk rating

“…Previous works on networks of firms focussed mainly on ownership relations [6][7][8][9][10], or dealt with the theoretical modelling of other types of relation [11]. Exceptions are the empirical studies on the Japanese economic firm-to-firm network [12,13], where links represent buyer-supplier relationship.…”

Distributed Company Control in Company Shareholding Graphs

“…The Italian ownership graph is characterized by a main large weakly connected component. As it shown in Figure 1 (from [24] and sometimes referred to as "the lung graph"), it contains the main 12 shareholding companies, with the highest out-degree. Six of them own more than 200 other companies (the right lung), whereas another group of six (the left lung) owns in turn a similar number.…”

“…Yet, to the best of our knowledge, the algorithms that have been proposed so far to solve the company control problem, in both the technical [24] and the economics [11] communities, are sequential and, unfortunately, do not meet the needs of the real-world applications, which require highly parallelizable methods to support a distributed version of company control, with the following desiderata:…”

“…Figure 1: Subgraph of Italian ownership graph from [24], with the 12 shareholders having the highest out-degree.…”

Resolution of ranking hierarchies in directed networks

“…We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit.It is important to stress that the concept of ranking hierarchy we employ in this paper, introduced in [34], and further developed in [18,21,14,36,32], models graphs, representing for example social organisations, as command structure or influential communities.Related literature sharing a similar definition of hierarchy includes [39,38,24,5,22]. This concept is therefore very different from the more common definition of nested hierarchy in networks, studied for example in [3,4,25,31], where low-level communities of nodes are nested into bigger ones, in a way directly associated with hierarchical clustering.…”