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Area of Science:

  • Graph theory
  • Information theory
  • Network science

Background:

  • Measuring network and graph complexity is crucial in scientific research.
  • Kolmogorov complexity is a key metric for quantifying object complexity.
  • Existing methods for graph complexity assessment are limited.

Purpose of the Study:

  • To formalize a method for calculating an upper bound of Kolmogorov complexity for graphs and networks.
  • To identify and utilize simple graph structures (O(1) Kolmogorov complexity) as a basis for complexity estimation.
  • To develop an algorithm that captures graph non-randomness for complexity assessment.

Main Methods:

  • Identification of graphs with minimal Kolmogorov complexity (O(1)).
  • Development of a method leveraging simple graph structures to estimate complexity.
  • Algorithm design to process graph inputs and output Kolmogorov complexity upper bounds.

Main Results:

  • A novel method for estimating an upper bound of Kolmogorov complexity for graphs and networks has been established.
  • The method effectively utilizes inherent simple structures within graphs to quantify non-randomness.
  • The algorithm successfully captures features indicating a graph's position on the non-randomness spectrum.

Conclusions:

  • The proposed method provides a valuable tool for assessing graph and network complexity.
  • This approach can be applied to evaluate the performance of graph compression algorithms.
  • The findings contribute to a deeper understanding of complexity in network science and information theory.