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A combinatorial approach to graphlet counting.

Tomaž Hočevar1, Janez Demšar

  • 1Faculty of Computer and Information Science, University of Ljubljana, SI-1000 Ljubljana, Slovenia.

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Summary
This summary is machine-generated.

This study introduces a new combinatorial method for counting graphlets and node orbit signatures in networks. The approach significantly reduces computational complexity for analyzing network structures.

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Area of Science:

  • Network analysis
  • Computational graph theory

Background:

  • Graphlets (small-induced subgraphs) are valuable for network structure analysis.
  • Computational complexity hinders the widespread use of graphlet-based network analysis.

Purpose of the Study:

  • To develop a novel combinatorial method for efficiently counting graphlets and node orbit signatures.
  • To address the computational challenges in graphlet discovery and counting.

Main Methods:

  • A combinatorial method is proposed to count graphlets and node orbit signatures.
  • A system of equations is constructed to relate orbit counts from graphlets up to five nodes.
  • All orbit counts are computed by enumerating a single orbit type.

Main Results:

  • The proposed method enables the computation of all orbit counts by enumerating just one.
  • Practical time complexity in sparse graphs is reduced by an order of magnitude compared to enumeration-based algorithms.
  • This advancement facilitates more efficient network structure and node role analysis.

Conclusions:

  • The new combinatorial method offers a significant computational advantage for graphlet and orbit signature counting.
  • This facilitates broader application of graphlet analysis in understanding complex networks.
  • The method enhances the exploration of global and local network structures and individual node roles.