Before revision:  We assume that, apart from the heterogeneity induced by the degree sequence itself, the network is homogeneous, so that its  link density can be estimated by sampling subsets of nodes with representative density.
After revision:  We assume that, apart from the heterogeneity induced by the degree sequence itself, the network is homogeneous, so that its (global) link density can be estimated by sampling subsets of nodes with representative density.