In this paper we present a generalized model for network growth that links the microscopical agent strategies with the large scale behavior. This model is intended to reproduce the largest number of features of the Internet network at the Autonomous System (AS) level. Our model of network grows by adding both new vertices and new edges between old vertices. In the latter case a ``rewarding attachment'' takes place mimicking the disassortative mixing between small routers to larger ones. We find a good agreement between experimental data and the model for the degree distribution, the betweenness distribution, the clustering coefficient and the correlation functions for the degrees.