Solving the Bipartite Graph Matching Problem for Atom Mappings As input the atom mapper uses two molecule conformations. First, the two conformations A and B are translated into independent sets of nodes N A and N B based on the coordinates indicating the atom positions of the molecules. Next, a complete weighted bipartite graph is calculated, by generating a full distance matrix of each node in N A to each node in N B (Figure ). This step is followed by a filtering step, that removes edges that have a distance weight longer than a given threshold (default: 0.95 Å), resulting in a sparser bipartite graph (Figure -2). The final perfect matching problem is solved with the Kuhn-Munkres algorithm for optimal linear-sum-assignments. The algorithm reduces the sparse bipartite graph edges to a perfect matching of this graph, where each node of the graph has a degree of one (Figure -3). The gained atom pair set p AB , can be further reduced on rules-based filters (i.e. by not allowing ring-breaking/ring-size changes in the atom-pair sets; more below).