In this paper, the authors provide a description of quantitative graph theory, which is a relatively new branch of graph theory. The key feature of this branch is its measurement approach to quantifying the structural information of networks. It deals with graph-theoretical and statistical network analysis. The research in this area is quite interesting, as classical graph theory involves deterministic analysis and its other aspect involves probabilistic analysis.

The authors describe various methods used in quantitative graph theory, including their applications. The first among them is comparative graph analysis, which deals with the structural similarity or distance between networks. The second method--graph characterization--investigates network complexity with the help of some numerical graph invariants. The authors also suggest some software and tools for the effective analysis of different graph similarity measures and graph distance measures.

The paper provides a basic introduction to this new field of study and ample references to the necessary related literature. It is informative and worth reading.