Network partition via a bound of the spectral radius

Based on the density of connections between the nodes of high degree, we introduce two bounds of the spectral radius. We use these bounds to split a network into two sets, one of these sets contains the high degree nodes, we refer to this set as the spectral--core. The degree of the nodes of the subnetwork formed by the spectral--core gives an approximation to the top entries of the leading eigenvector of the whole network. We also present some numerical examples showing the dependancy of the spectral--core with the assortativity coefficient, its evaluation in several real networks and how the properties of the spectral--core can be used to reduce the spectral radius.