Quantification and statistical analysis of topological features of recursive trees

Abstract

Some topological features of recursive trees are quantified by exploiting the decomposition of directed graphs into a suitable combination of starlike hierarchical and three-edge cyclic components. This approach requires the adoption of the formalism of weighted directed graphs and allows us to quantify the proportion of hierarchical and hidden cyclic components. Using this concept, we can introduce new local parameters and global measures that quantify certain topological features of recursive trees. The average values of some of these measures over the general set of same-sized recursive trees are also determined.