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We study the network dismantling problem, which consists in determining a minimal set of vertices whose removal leaves the network broken into connected components of sub-extensive size. For a large class of random graphs, this problem is tightly connected to the decycling problem (the removal of vertices leaving the graph acyclic). Exploiting this connection and recent works on epidemic spreading we present precise predictions for the minimal size of a dismantling set in a large random graph with a prescribed (light-tailed) degree distribution. Building on the statistical mechanics perspective we propose a three-stage Min-Sum algorithm for efficiently dismantling networks, including heavy-tailed ones for which the dismantling and decycling problems are not equivalent. We also provide further insights into the dismantling problem concluding that it is an intrinsically collective problem and that optimal dismantling sets cannot be viewed as a collection of individually well performing nodes.
We propose a maximally disassortative (MD) network model which realizes a maximally negative degree-degree correlation, and study its percolation transition to discuss the effect of a strong degree-degree correlation on the percolation critical behav
This paper explores a variety of strategies for understanding the formation, structure, efficiency and vulnerability of water distribution networks. Water supply systems are studied as spatially organized networks for which the practical applications
Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that
Individual heterogeneity is a key characteristic of many real-world systems, from organisms to humans. However its role in determining the systems collective dynamics is typically not well understood. Here we study how individual heterogeneity impact
Network growth processes can be understood as generative models of the structure and history of complex networks. This point of view naturally leads to the problem of network archaeology: reconstructing all the past states of a network from its struc