The emergence of a nanofiller network in polymer nanocomposites yields unique rheological signatures in the form of a low-frequency plateau in the viscoelastic moduli. These phenomena are difficult to model using conventional viscoelastic models, making quantitative assessments of the mechanics of nanofiller-percolated polymer nanocomposites difficult. Here we demonstrate that fractional viscoelastic models can be utilized to accurately model the time-dependent mechanical properties of a model nanocomposite gel over six decades of frequencies. Such modelling endeavours yield a single parameter representing the elasticity of the percolated nanoparticle network, GNP, which depends strongly on the concentration of nanoparticles in the network. Small-angle scattering experiments confirm that the emergence of GNP with increasing nanoparticle concentrations is directly correlated with nanoparticle connectivity, which manifests through an increase in the periodicity of the spacings between the nanoparticles. These findings open new avenues to quantitatively understand the complex viscoelasticity of physical gels and model the connectivity and elasticity of nanofiller networks in polymer nanocomposites.