  Graphs are interesting structures: extremely useful to depict real-life
problems, extremely easy to understand given a sketch, extremely complicated to
represent formally, extremely complicated to compare. Phylogeny is the study of
the relations between biological entities. From it, the interest in comparing
tree graphs grew more than in other fields of science. Since there is no
definitive way to compare them, multiple distances were formalized over the
years since the early sixties, when the first effective numerical method to
compare dendrograms was described. This work consists of formalizing,
completing (with original work) and give a universal notation to analyze and
compare the discriminatory power and time complexity of computing the thirteen
here formalized metrics. We also present a new way to represent tree graphs,
reach deeper in the details of the Geodesic Distance and discuss its worst-case
time complexity in a suggested implementation. Our contribution ends up as a
clean, valuable resource for anyone looking for an introduction to comparative
metrics for tree graphs.
