Some of our recent developments and applications of algorithmic graph theory for extracting the physical and chemical properties of materials from molecular dynamics simulations are presented. From the chemical viewpoint, the power of graph theory is illustrated in the search for a catalyst's active sites at a silica solid surface. From the physical viewpoint, we present graph algorithms that recognize the structural motifs that exist at the silica/liquid water interface. Statistical analyses of the instances of these surface–water motifs provide a detailed understanding of the structures and dynamics at the aqueous interface.@en