  Although algebraic graph theory based models have been widely applied in
physical modeling and molecular studies, they are typically incompetent in the
analysis and prediction of biomolecular properties when compared with other
quantitative approaches. There is a need to explore the capability and
limitation of algebraic graph theory for molecular and biomolecular modeling,
analysis, and prediction. In this work, we propose novel algebraic graph
learning (AGL) models that encode high-dimensional physical and biological
information into intrinsically low-dimensional representations. The proposed
AGL model introduces multiscale weighted colored subgraphs to describe crucial
molecular and biomolecular interactions via graph invariants associated with
the graph Laplacian, its pseudo-inverse, and adjacent matrix. Additionally, the
AGL models are incorporated with an advanced machine learning algorithm to
connect the low-dimensional graph representation of biomolecular structures
with their macroscopic properties. Three popular protein-ligand binding
affinity benchmarks, namely CASF-2007, CASF-2013, and CASF-2016, are employed
to validate the accuracy, robustness, and reliability of the present AGL model.
Numerical results indicate that the proposed AGL method outperforms the other
state-of-the-art methods in the binding affinity predictions of the
protein-ligand complexes.
