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, such as the degree or the betweenness. 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. In this seminar I will introduce a novel mathematical framework that fills this gap: networks are enriched with features and their nodes are removed according to the importance in the feature space. We will discuss features of different nature, from ones related to the network construction to ones related to dynamical processes such as epidemic spreading. In this way, we not only provide a natural generalization of percolation but, more importantly, this framework offers an accurate way to test the robustness of networks in realistic scenarios.
More information can be found at https://www.nature.com/articles/s41467-021-22721-z.
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