  Nowadays, the coupling of electronic structure and machine learning
techniques serves as a powerful tool to predict chemical and physical
properties of a broad range of systems. With the aim of improving the accuracy
of predictions, a large number of representations for molecules and solids for
machine learning applications has been developed. In this work we propose a
novel descriptor based on the notion of molecular graph. While graphs are
largely employed in classification problems in cheminformatics or
bioinformatics, they are not often used in regression problem, especially of
energy-related properties. Our method is based on a local decomposition of
atomic environments and on the hybridization of two kernel functions: a graph
kernel contribution that describes the chemical pattern and a Coulomb label
contribution that 1encodes finer details of the local geometry. The accuracy of
this new kernel method in energy predictions of molecular and condensed phase
systems is demonstrated by considering the popular QM7 and BA10 datasets. These
examples show that the hybrid localized graph kernel outperforms traditional
approaches such as, for example, the smooth overlap of atomic positions (SOAP)
and the Coulomb matrices.
