Relationship between B-factor and average shortest path in the protein structure

Protein structural flexibility is important for catalysis, binding, protein design, and allostery. Some simple methods have recently been introduced to compute protein flexibility directly from the protein structure without any mechanical models. For example the atomic mean square displacement (or B-factor) is related to the number of neighboring atoms. The protein structure can be modeled as a graph where nodes represent atoms and edges can be defined by Delaunay tessellation procedure with weight equal to d2 where d is the Euclidean distance between pair of atoms. In this study, we show that the average of shortest path for each atom in this graph is related to the B-factor.