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The smallest positive eigenvalue of the Laplacian of a network is called thespectral gap and characterizes various dynamics on networks. We proposemathematical programming methods to maximize the spectral gap of a givennetwork by removing a fixed number of nodes. We formulate relaxed versions ofthe original problem using semidefinite programming and apply them to examplenetworks.

Application of semidefinite programming to maximize the spectral gap produced by node removal