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    Dynamics of k-core percolation

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    In many network applications nodes are stable provided they have at least k neighbors, and a network of k-stable nodes is called a k-core. The vulnerability to random attack is characterized by the size of culling avalanches which occur after a randomly chosen k-core node is removed. Simulations of lattices in two, three and four dimensions, as well as small world networks, indicate that power-law avalanches occur in first order k-core systems, while truncated avalanches are characteristic of second order cases.Comment: 4 pages, 3 figure
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