The connectivity Omstein-Zernike formalism, together with the polymer reference interaction site model (PRISM), is employed to describe connectivity and network formation in mixtures of spheres and polymers. Results are presented for the percolation of spheres induced by both flexible coil-like and rigid rod-like linear polymers; the Percus-Yevick (PY) approximation is used throughout. Our results are compared with predictions based on the adhesive hard sphere (AHS) model, and correlations with the polymer-mediated second virial coefficient between spheres are discussed.