Allosteric proteins bind an effector molecule at one site resulting in a functional change at a second site. We hypothesize that allosteric communication in proteins relies upon networks of quaternary (collective, rigid-body) and tertiary (residue-residue contact) motions. We argue that cyclic topology of these networks is necessary for allosteric communication. An automated algorithm identifies rigid bodies from the displacement between the inactive and the active structures and constructs "quaternary networks" from these rigid bodies and the substrate and effector ligands. We then integrate quaternary networks with a coarse-grained representation of contact rearrangements to form "global communication networks" (GCNs). The GCN reveals allosteric communication among all substrate and effector sites in 15 of 18 multidomain and multimeric proteins, while tertiary and quaternary networks exhibit such communication in only 4 and 3 of these proteins, respectively. Furthermore, in 7 of the 15 proteins connected by the GCN, 50% or more of the substrate-effector paths via the GCN are "interdependent" paths that do not exist via either the tertiary or the quaternary network. Substrate-effector "pathways" typically are not linear but rather consist of polycyclic networks of rigid bodies and clusters of rearranging residue contacts. These results argue for broad applicability of allosteric communication based on structural changes and demonstrate the utility of the GCN. Global communication networks may inform a variety of experiments on allosteric proteins as well as the design of allostery into non-allosteric proteins.