2014/05/31 by Giulia Menichetti, Luca Dall'Asta, Luca Dall’Asta +1 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Betweenness centrality #Centrality #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Controllability #Degree (music) #Degree distribution #Fraction (chemistry) #Infinitesimal #Mathematical analysis #Mathematics #Network controllability #Neural Networks Stability and Synchronization #Opinion Dynamics and Social Influence #Physics #Statistics #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1103/physrevlett.113.078701
published as Phys. Rev. Lett. 113, 078701 (2014) · (9 pages, 4 figures)
openalex publication_date 2014/08/13 · arxiv created 2014/08/14 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The problem of controllability of the dynamical state of a network is central in network theory and has wide applications ranging from network medicine to financial markets. The driver nodes of the network are the nodes that can bring the network to the desired dynamical state if an external signal is applied to them. Using the framework of structural controllability, here, we show that the density of nodes with in degree and out degree equal to one and two determines the number of driver nodes in the network. Moreover, we show that random networks with minimum in degree and out degree greater than two, are always fully controllable by an infinitesimal fraction of driver nodes, regardless of the other properties of the degree distribution. Finally, based on these results, we propose an algorithm to improve the controllability of networks.