This paper reviews some of our developments in algorithmic graph theory, with some applications in physical chemistry and catalysis. Two levels of granularity in the topological graphs have been developed: atomistic 2D-MolGraphs and coarse-grained polygraphs of H-bonded cycles. These graphs have been implemented with the key algorithms of isomorphism and polymorphism, in order to analyze molecular dynamics simulations of complex molecular systems. These topological graphs are transferable without modification from “simple” gas molecules, to liquids, to more complex inhomogeneous interfaces between solid and liquid for instance. We show hereby that the use of algorithmic graph theory provides a direct and fast approach to identify the actual conformations sampled over time in a trajectory. Graphs of transitions can also be extracted, showing at first glance all the interconversions over time between these conformations. H-bond networks in condensed matter molecular systems such as aqueous interfaces are shown to be easily captured through the topological graphs. We also show how the 2D-MolGraphs can easily be included in automated high-throughput in silico reactivity workflows, and how essential they are in some of the decisive steps to be taken in these workflows. The coarse-grained polygraphs of H-bonded cycles are shown to be essential topological graphs to analyze the dynamics of flexible molecules such as a hexapeptide in gas phase.