A cyclic peptide contains a covalently closed ring incorporating part or all of its amino acid residue chain. A head-to-tail ring joins the usual terminal amino and carboxyl groups through a peptide bond. Other ring architectures involve side chains or different linkages, so the positions and chemical types of the closures must be specified.[ref]
Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names 2013 by IUPAC. Peptide nomenclature, homodetic and heterodetic cyclic peptides
For a topology example, a linear unbranched chain of six amino acid residues has five backbone peptide bonds. Closing that chain head-to-tail adds a sixth bond and removes its free N-terminus and C-terminus. It preserves the residue order around the ring, although choosing a different residue as the written starting point does not create a new ring. This counting example does not imply that every chosen sequence readily forms such a ring.
Alpha-amanitin supplies a biological example: it combines a cyclic eight-residue framework with an additional sulfur-containing bridge. Its shape is therefore more constrained than residue count alone reveals.[ref]
Alpha-Amanitin in PubChem. CID 9543442, structural description
Ring closure changes accessible conformations; its effects on stability, binding and biological activity depend on the particular peptide and its surroundings. New to topics? Read the docs here!