In both ordinary networks and hypergraphs, the percolation threshold exhibits nonmonotonic dependence on assortativity, with moderately disassortative configurations often the most fragile under random node removal.
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Using a Langevin field theory on networks, the authors claim pairwise mechanisms are formally equivalent to higher-order contagion, pairwise terms dominate at coarse scales, and spectral dimension controls the phase transition.
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Nonmonotonic percolation threshold in correlated networks and hypergraphs
In both ordinary networks and hypergraphs, the percolation threshold exhibits nonmonotonic dependence on assortativity, with moderately disassortative configurations often the most fragile under random node removal.
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Higher-order contagion processes in 3.99 dimensions
Using a Langevin field theory on networks, the authors claim pairwise mechanisms are formally equivalent to higher-order contagion, pairwise terms dominate at coarse scales, and spectral dimension controls the phase transition.