We investigate the relationships between structure and linear viscoelasticity of a model polymer nanocomposite system based on a mixture of fumed silica nanoparticles and polystyrene. Alterations in the viscoelastic behavior are attributed to the structuring of primary silica aggregates. Above a critical filler volume fraction, a space-filling network builds up as the result of cluster aggregation, and the complex frequency-dependence of the moduli is simplified by splitting the viscoelasticity of the composites into the independent responses of the suspending polymer melt and the filler network. Specifically, we present a refinement of a two-component model recently proposed for attractive colloidal suspensions, in which hydrodynamic effects related to the presence of the filler are properly taken into account using the concept of shear stress equivalent deformation. Our approach, validated through the building of a master curve of the elastic modulus for samples of different composition, allows the estimation of the elasticity of samples in which the filler network is too tenuous to be appreciated through a simple frequency scan. In addition, the structure of the filler network is studied using both the percolation and fractal approaches, and the reliability of the critical parameters is discussed. We expect that our analysis may be useful for understanding the behavior of a wide variety of complex fluids where the elasticity of the components may be superimposed.