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

Abstract

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

1 figure. Short paper presented in CompleNet, Berlin, March 13-15 (2013)