Process topologies are associated with communicators; they are optional attributes that can be given to an intracommunicator (not to an intercommunicator).
Recall that processes in a group are ranked from 0 to n-1. This linear ranking often reflects nothing of the logical communication pattern of the processes, which may be, for instance, a 2- or 3-dimensional grid. The logical communication pattern is referred to as a virtual topology (separate and distinct from any hardware topology). In MPI, there are two types of virtual topologies that can be created: Cartesian (grid) topology and graph topology.
You can use virtual topologies in your programs by taking physical processor organization into account to provide a ranking of processors that optimizes communications.