The influence of interparticle interactions on the fractal structure of gels formed from networks of aggregated spherical particles is investigated by Brownian dynamics computer simulation. In moderately concentrated systems of particles interacting with non-bonded Lennard-Jones interactions, restructuring of the network towards a phase-separated state leads to time-dependent changes in the primary cluster mass and in the intermediate-range fractal dimensionality. Using a colloid-type interaction potential of shorter attractive range leads to the same coarse network structure but a slower rate of restructuring. Networks derived from simulations incorporating flexible irreversible bond formation and repulsive interparticle interactions have a polymer gel character with regular spacings between chains and a small average pore size. Systems exhibiting both bonding and attractive non-bonding interparticle forces can produce permanent fine or coarse microstructures depending on the relative rates of cross-linking and phase separation. Structural features of the simulated gels have much in common with model food particle gels formed from aggregated protein particles.