Exploring Topological Properties of NMR Graphs

In this paper we explore the topological properties of graphs derived from nuclear magnetic resonance (NMR) restraint data. Only the distance bound data is considered, connecting nodes only if the file contains a bound for the corresponding inter-atomic distance. Since NMR provides bounds for spatially-close atom pairs, the structure of the NMR graph depends heavily on the molecule´s 3D shape. Therefore, understanding NMR graph topology is relevant to 3D structure prediction. We examine NMR graphs for nine molecules, sizes ranging between 195 and 1178 nodes. Three categories of topological properties are studied: connected components, diameter, and node-degree sequence. Several interesting observations emerged when relating the diameter and maximum degree to the size of the graph.