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.