  This paper is concerned with the shape invariants satisfied by the
communication topology of {\pi}-terms, and the automatic inference of these
invariants. A {\pi}-term P is hierarchical if there is a finite forest T such
that the communication topology of every term reachable from P satisfies a
T-shaped invariant. We design a static analysis to prove a term hierarchical by
means of a novel type system that enjoys decidable inference. The soundness
proof of the type system employs a non-standard view of {\pi}-calculus
reactions. The coverability problem for hierarchical terms is decidable. This
is proved by showing that every hierarchical term is depth-bounded, an
undecidable property known in the literature. We thus obtain an expressive
static fragment of the {\pi}-calculus with decidable safety verification
problems.
