In this paper, we review classical and recent developments on comparability
graphs. Also, we demonstrate that comparability graphs are useful to analyze molecular
graphs by presenting classical and new results. In fact, it turns out that the underlying
model is quite general and, hence, could be used to analyze any kind of network data.
Keywords: Comparability graphs, chemical graph, topological indices, molecular
descriptor, structural complexity, graph entropy, Shannon information content,
quantitative network analysis, information-theoretic measures, structural similarity,
similarity measures, graph edit distance, similarity matrix, correlation matrix.
