Similarity studies are important for chemistry and their applications range
from the periodic table to the screening of large databases in the searching for new
drugs. In this later case, it is assumed that similarity in molecular structure is related to
similarity in reactivity. However, we state that structural formulas can be regarded as
abstract representations emerging from the analysis of large amounts of data upon
chemical reactivity. Hence, chemical formulas such as organic functions are not direct
pictures of the atomic constitution of matter, but signs used to represent similarity in the
reactivity of a class of substances. Therefore, reactivity, rather than molecular structure,
becomes the fundamental feature of chemical substances. As reactivity is important,
chemical identity is given by the relations substances establish with each other, giving
place to a network of chemical reactions. We explore similarity in the network rather
than in molecular structure. By characterising each substance in terms of the related
ones, we show how Category Theory helps in this description. Afterwards, we study the
similarity among substances using topological spaces, which leads us to concepts such
as closure and neighbourhood, which formalise the intuition of things lying somewhere
near around. The second focus of the chapter is the exploration of the potential of
closure operators, and of topological closures in particular, as more general descriptors
of chemical similarity. As we introduce the formalism, we develop a worked example,
concerning the analysis of similarity among chemical elements regarding their ability to
combine into binary compounds. The results show that several of the trends of chemical
elements are found through the current approach.
Keywords: Binary compounds, category theory, chemical classification, chemical
networks, closure, closure operators, directed hypergraphs, formal concept
analysis, graph theory, network theory, order theory, periodic table, reaction
networks, similarity, topology.
