Abstract
Many social, technological, and biological systems with asymmetric interactions display a variety of collective phenomena, such as opinion formation and synchronization. This has motivated much research on the dynamical impact of local and mesoscopic structure in directed networks. However, the unique constraints imposed by the global organization of directed networks remain largely undiscussed. Here, we control the global organization of directed Erdős–Rényi networks, and study its impact on the emergence of synchronization and ferromagnetic ordering, using Kuramoto and Ising dynamics. In doing so, we demonstrate that source nodes – peripheral nodes without incoming links – can disrupt or entirely suppress the emergence of collective states in directed networks. This effect is imposed by the bow-tie organization of directed networks, where a large connected core does not uniquely ensure the emergence of collective states, as it does for undirected networks.
Highlights
If sources make up the entire IN component, they will act as a field on some subset of CORE nodes, with dynamics differing in the choice of dynamical parameters, link properties, and initial conditions
We consider a simple toy model based on directed Erdős–Rényi (ER) networks, where the structural features of interest are determined by the mean in-degree〈qin〉3, starting with the emergence of the core in the netwWohrkenatd〈eqtienr〉m=in1in(pgehrocwolastoiounrcpesoiinntf)lu. ence the collective dynamics of the core, we must consider how CORE nodes connect to each other, the number of SOURCE nodes relative to that of CORE nodes, and how the former connect to the latter
For any directed network where the IN component is entirely composed of SOURCE nodes, the dynamics of the SOURCE nodes are formally equivalent to external fields, which act directly on any number of CORE nodes
Summary
The core of this architecture is the network’s largest strongly connected component, and all remaining components – the periphery – are hierarchically defined in relation to the core. The infectious potential of individual nodes in animal trade networks has been determined by their classification within the bow-tie topology of these networks[7,8] This architecture is common in biological networks[9], and has been reported in gene regulatory networks[10], metabolic networks[11], and neuronal networks[12,13]. Source nodes may have distinct internal dynamics, potentially capturing specific functional behavior, such as the tweet-sharing activity of notable source nodes in the Twitter follow network, e.g. the Dalai Lama and Eminem (at the time of writing), who have millions more followers than the average user[20] and may, for example, be more selective about the content they share, or have a different impact depending on the emotional and cognitive content of their tweets
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
