<p><b>The mapping of chemical space by the enumeration of
graphs generates an infinite number of molecules, yet the experimental
exploration of known chemical space shows that it appears to become sparser as
the molecular weight of the compounds increases. What is needed is a way to
explore chemical space that exploits the information encoded in known molecules
to give access to unknown chemical space by building on the common conserved
structures found in related families of molecules. Molecular assembly theory
provides an approach to explore and compare the intrinsic complexity of
molecules by the minimum number of steps needed to build up the target graphs, and
here we show this can be applied to networks of molecules to explore the
assembly properties of common motifs, rather than just focusing on molecules in
isolation. This means molecular assembly theory can be used to define a tree of
assembly spaces, allowing us to
explore the accessible molecules connected to the tree, rather than the entire
space of possible molecules. This approach provides a way to map the
relationship between the molecules and their common fragments and thus measures
the distribution of structural information collectively embedded in the
molecules. We apply this approach to prebiotic chemistry, specifically the
construction of RNA, and a family of opiates and plasticizers, as well as to
gene sequences. This analysis allows us to quantify the amount of external
information needed to assemble the tree and identify and predict new components
in this family of molecules, based on the contingent information in the
assembly spaces.</b></p>