Residue interaction networks and loop motions are important for catalysis in dihydrofolate reductase (DHFR). Here, we investigate the effects of ligand binding and chain connectivity on network communication in DHFR. We carry out systematic network analysis and molecular dynamics simulations of the native DHFR and 19 of its circularly permuted variants by breaking the chain connections in ten folding element regions and in nine nonfolding element regions as observed by experiment. Our studies suggest that chain cleavage in folding element areas may deactivate DHFR due to large perturbations in the network properties near the active site. The protein active site is near or coincides with residues through which the shortest paths in the residue interaction network tend to go. Further, our network analysis reveals that ligand binding has "network-bridging effects" on the DHFR structure. Our results suggest that ligand binding leads to a modification, with most of the interaction networks now passing through the cofactor, shortening the average shortest path. Ligand binding at the active site has profound effects on the network centrality, especially the closeness.