Topological self-similarity on the random binary-tree model

Abstract

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented.

References in corpus (3)

• Community analysis in social networks
• On the topological classification of binary trees using the Horton-Strahler index
• Numerical Approach to Central Limit Theorem for Bifurcation Ratio of Random Binary Tree

Cited by in corpus (4)

• Large deviation theorem for branches of the random binary tree in the Horton-Strahler analysis
• Central limit theorem for the Horton-Strahler bifurcation ratio of general branch order
• Reductions of Binary Trees and Lattice Paths induced by the Register Function
• The Register Function and Reductions of Binary Trees and Lattice Paths