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Nodal-statistics-based equivalence relation for graph collections.

Lucrezia Carboni1,2, Michel Dojat2, Sophie Achard1

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Summary
This summary is machine-generated.

Identifying node roles in complex networks is challenging. This study introduces a new method using nodal statistics to reveal distinct node roles and compare network structures, applicable to brain connectivity analysis.

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Area of Science:

  • Graph theory
  • Network science
  • Computational neuroscience

Background:

  • Node role explainability in complex networks is critical across disciplines like social science, neuroscience, and computer science.
  • Existing methods often focus on single structural properties, leaving the identification of node roles with multiple properties and network instances underexplored.

Purpose of the Study:

  • To develop a novel method for identifying and quantifying node roles in complex networks using collections of nodal statistics.
  • To introduce new global graph measures (power coefficient, orthogonality score) for evaluating nodal statistics collections.
  • To compare graph structures and assess node role distinctiveness within families of graphs.

Main Methods:

  • Defined a new equivalence relation on graph nodes based on collections of nodal statistics.
  • Introduced the power coefficient and orthogonality score as global graph measures.
  • Developed a method based on structural patterns to assign a distinctiveness value to nodes within a graph family.
  • Validated the method on generative graph models and real-world human brain functional connectivity data.

Main Results:

  • The proposed method effectively identifies node roles and quantifies their distinctiveness.
  • Nodal statistics differences are shown to depend on the underlying graph structure.
  • Analysis of human brain functional connectivity reveals complexity at global and nodal levels.
  • The method successfully detected homotopy in healthy controls and quantified differences between comatose patients and healthy individuals.

Conclusions:

  • The new method provides a robust framework for node role explainability in complex networks, especially when multiple nodal statistics are considered.
  • The approach offers valuable insights into the structural complexity of human brain functional connectivity.
  • This method has potential applications in clinical neuroscience for differentiating patient groups based on network properties.