Topological complexity of crystal structures: quantitative approach

The topological complexity of a crystal structure can be quantitatively evaluated using complexity measures of its quotient graph, which is defined as a projection of a periodic network of atoms and bonds onto a finite graph. The Shannon information-based measures of complexity such as topological information content, I_G, and information content of the vertex-degree distribution of a quotient graph, I_vd, are shown to be efficient for comparison of the topological complexity of polymorphs and chemically related structures. The I_G measure is sensitive to the symmetry of the structure, whereas the I_vd measure better describes the complexity of the bonding network.