Percolation on feature-enriched interconnected systems

Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or sequentially ordered by specific topological descriptors. However, in the vast majority of empirical applications, it is required to dismantle the network following more sophisticated protocols, for instance, by combining topological properties and non-topological node metadata. We propose a novel mathematical framework to fill this gap: networks are enriched with features and their nodes are removed according to the importance in the feature space. We consider features of different nature, from ones related to the network construction to ones related to dynamical processes such as epidemic spreading. Our framework not only provides a natural generalization of percolation but, more importantly, offers an accurate way to test the robustness of networks in realistic scenarios. Network robustness is usually assessed following topological criteria, but disregards the role played by non-topological information. Artime et al. propose a flexible percolation framework that overcomes this limitation and combines both dimensions, offering new ways to protect real systems.

Automated summary

The study introduces a new mathematical framework for evaluating network robustness, enriching network features and removing nodes based on their importance in the feature space. This framework not only generalizes the percolation model, but also provides an accurate way to test network robustness under more realistic conditions.