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Tree asymmetry--a sensitive and practical measure for binary topological trees.

J Van Pelt1, H B Uylings, R W Verwer

  • 1Netherlands Institute for Brain Research, Amsterdam.

Bulletin of Mathematical Biology
|September 1, 1992
PubMed
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Tree asymmetry, a measure of binary tree topology, effectively distinguishes between different branching patterns. Its statistical properties, studied via a growth model, show near-independence from tree size, making it practical for analyzing complex structures like neuronal branching.

Area of Science:

  • Computational Biology
  • Network Science
  • Data Analysis

Background:

  • Binary tree topology is often analyzed using measures of structural complexity.
  • Existing measures may not be sufficiently sensitive to subtle topological differences or easily applicable to diverse datasets.

Purpose of the Study:

  • To introduce and evaluate tree asymmetry as a robust measure for characterizing binary tree topology.
  • To assess the statistical properties of tree asymmetry using a binary tree growth model.
  • To demonstrate the utility of tree asymmetry in analyzing real-world branching patterns, such as neuronal structures.

Main Methods:

  • Definition of tree asymmetry as the mean asymmetry of partitions within a binary tree.
  • Statistical analysis of tree asymmetry using a stochastic binary tree growth model.

Related Experiment Videos

  • Application of the tree asymmetry measure to empirical datasets of neuronal branching patterns.

    • Main Results:

    • Tree asymmetry is sensitive to topological variations in binary trees.
    • The expected value of tree asymmetry under the growth model is largely independent of tree size.
    • The variance of tree asymmetry in observed neuronal branching patterns closely matches the model's predictions.

    Conclusions:

    • Tree asymmetry is a simple yet powerful metric for quantifying binary tree topology.
    • Its size-independence and sensitivity make it suitable for comparative analyses of branching patterns.
    • The growth model accurately predicts the variability observed in empirical neuronal branching structures.