  For more than 150 years the structure of the periodic system of the chemical
elements has intensively motivated research in different areas of chemistry and
physics. However, there is still no unified picture of what a periodic system
is. Herein, based on the relations of order and similarity, we report a formal
mathematical structure for the periodic system, which corresponds to an ordered
hypergraph. It is shown that the current periodic system of chemical elements
is an instance of the general structure. The definition is used to devise a
tailored periodic system of polarizability of single covalent bonds, where
order relationships are quantified within subsets of similar bonds and among
these classes. The generalised periodic system allows envisioning periodic
systems in other disciplines of science and humanities.
