Various company interactions can be described by networks, for instance the ownership networks and the board membership networks. To understand the ecosystem of companies, these interactions cannot be seen in isolation. For this purpose we construct a new multilayer network of interactions between companies in Germany and in the United Kingdom, combining ownership links, social ties through joint board directors, R\&D collaborations and stock correlations in one linked multiplex dataset. We describe the features of this network and show there exists a non-trivial overlap between these different types of networks, where the different types of connections complement each other and make the overall structure more complex. This highlights that corporate control, boardroom influence and other connections have different structures and together make an even smaller corporate world than previously reported. We have a first look at the relation between company performance and location in the network structure.

 

The Multilayer Structure of Corporate Networks
Jeroen van Lidth de Jeude, Tomaso Aste, Guido Caldarelli

Source: arxiv.org

The Kuramoto model, originally proposed to model the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior of large heterogeneous groups of dynamical units whose states are characterized by a scalar angle variable. One such application in which we are interested is the alignment of orientation vectors among members of a swarm. Despite being commonly used for this purpose, the Kuramoto model can only describe swarms in two dimensions, and hence the results obtained do not apply to the often relevant situation of swarms in three dimensions. Partly based on this motivation, as well as on relevance to the classical, mean-field, zero-temperature Heisenberg model with quenched site disorder, in this paper we study the Kuramoto model generalized to D dimensions. We show that in the important case of three dimensions, as well as for any odd number of dimensions, the D-dimensional generalized Kuramoto model for heterogeneous units has dynamics that are remarkably different from the dynamics in two dimensions. In particular, for odd D the transition to coherence occurs discontinuously as the interunit coupling constant  K is increased through zero, as opposed to the  D=2 case (and, as we show, also the case of even D) for which the transition to coherence occurs continuously as K increases through a positive critical value Kc. We also demonstrate the qualitative applicability of our results to related models constructed specifically to capture swarming and flocking dynamics in three dimensions.

 

Continuous versus Discontinuous Transitions in the D
-Dimensional Generalized Kuramoto Model: Odd
D is Different
Sarthak Chandra, Michelle Girvan, and Edward Ott
Phys. Rev. X 9, 011002 – Published 3 January 2019

Source: journals.aps.org

Many time-evolving systems in nature, society and technology leave traces of the interactions within them. These interactions form temporal networks that reflect the states of the systems. In this work, we pursue a coarse-grained description of these systems by proposing a method to assign discrete states to the systems and inferring the sequence of such states from the data. Such states could, for example, correspond to a mental state (as inferred from neuroimaging data) or the operational state of an organization (as inferred by interpersonal communication). Our method combines a graph distance measure and hierarchical clustering. Using several empirical data sets of social temporal networks, we show that our method is capable of inferring the system’s states such as distinct activities in a school and a weekday state as opposed to a weekend state. We expect the methods to be equally useful in other settings such as temporally varying protein interactions, ecological interspecific interactions, functional connectivity in the brain and adaptive social networks.

 

Detecting sequences of system states in temporal networks
Naoki Masuda & Petter Holme 
Scientific Reports volume 9, Article number: 795 (2019)

Source: www.nature.com

Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency matrix) description of the network structure. While extensive approaches—such as the state-of-the-art message passing approximation—typically yield more accurate predictions, intensive approaches provide crucial insights on the role played by any given structural property in the outcome of dynamical processes. Here we introduce an intensive description that yields almost identical predictions to the ones obtained with the message passing approximation using bond percolation as a benchmark. Our approach distinguishes nodes according to two simple statistics: their degree and their position in the core-periphery organization of the network. Our near-exact predictions highlight how accurately capturing the long-range correlations in network structures allows easy and effective compression of real complex network data.

 

Percolation and the Effective Structure of Complex Networks
Antoine Allard and Laurent Hébert-Dufresne
Phys. Rev. X 9, 011023 – Published 5 February 2019

Source: journals.aps.org