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Updated: Apr 25, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
Published on: October 13, 2023
Network controllability is determined by the density of low in-degree and out-degree nodes
Giulia Menichetti1, Luca Dall'Asta2, Ginestra Bianconi3
1Department of Physics and Astronomy and INFN Sezione di Bologna, Bologna University, Viale Berti Pichat 6/2, 40127 Bologna, Italy.
Abstract:
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.
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