Improving robustness of spatial networks via reinforced nodes

Department of Physics, Bar-Ilan University - Ramat-Gan 52900, Israel

^(a) E-mail: Nir315@gmail.com
^(b) E-mail: bnaya.gross@gmail.com (corresponding author)

Received: 8 March 2023
Accepted: 30 May 2023

Abstract

Many real-world networks are embedded in space, and their resilience in the presence of reinforced nodes has not been studied. In this paper, we use a spatial network model with an exponential distribution of link length r and a characteristic length ζ to model such networks. We find that reinforced nodes can significantly increase the resilience of the networks, which varies with the strength of spatial embedding. We also study different reinforced node distribution strategies for improving the network's resilience. Interestingly, we find that the best strategy is highly dependent on the expected magnitude of failures which we analyze using percolation theory. Finally, we show that the reinforced nodes are analogous to an external field in the percolation phase transition and that their critical exponents satisfy Widom's relation.