Inevitable self-similar topology of binary trees and their diverse hierarchical density

Kyungrock Paik, P. Kumar

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Self-similar topology, which can be characterized as power law size distribution, has been found in diverse tree networks ranging from river networks to taxonomic trees. In this study, we find that the statistical self-similar topology is an inevitable consequence of any full binary tree organization. We show this by coding a binary tree as a unique bifurcation string. This coding scheme allows us to investigate trees over the realm from deterministic to entirely random trees. To obtain partial random trees, partial random perturbation is added to the deterministic trees by an operator similar to that used in genetic algorithms. Our analysis shows that the hierarchical density of binary trees is more diverse than has been described in earlier studies. We find that the connectivity structure of river networks is far from strict self-similar trees. On the other hand, organization of some social networks is close to deterministic supercritical trees.

Original languageEnglish
Pages (from-to)247-258
Number of pages12
JournalEuropean Physical Journal B
Volume60
Issue number2
DOIs
Publication statusPublished - 2007 Nov 1
Externally publishedYes

Fingerprint

Binary trees
topology
Topology
Rivers
Mathematical operators
Genetic algorithms
rivers
coding
genetic algorithms
strings

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials

Cite this

Inevitable self-similar topology of binary trees and their diverse hierarchical density. / Paik, Kyungrock; Kumar, P.

In: European Physical Journal B, Vol. 60, No. 2, 01.11.2007, p. 247-258.

Research output: Contribution to journalArticle

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