Despite the significant processes in the multi-scale studies of sand - rubber mixtures, the load-transfer mechanism within the soft-rigid granulate networks is highly unexplored. In this study, roles of sand and rubber particles in different contact networks subjected to constrained compression were investigated using DEM. The simulations were respectively calibrated using experimental data at element and grain scales, providing an opportunity to look at the role of rubber within whole granulate networks. When the behavior of mixtures is dominated by sand (rubber content <30%), the constitutive responses at sand-sand, sand-rubber and rubber-rubber contacts can be described by the Hertz contact model; within this range, the rubber majorly formulates the weak and intermediate contacts, but sliding fraction in the strong network increases with rubber content. A more homogeneous fabric and a lower deviatoric stress at the strong network were observed after rubber inclusion.