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Stochastic graph Voronoi tessellation reveals community structure.

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We introduce Voronoi cohesion, a novel network analysis measure based on graph-Voronoi diagrams. This method reveals large-scale network structures by analyzing shared Voronoi cells with randomly chosen centers.

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Area of Science:

  • Network science
  • Computational topology
  • Graph theory

Background:

  • Graph-Voronoi diagrams offer insights into network structures.
  • Existing similarity measures often lack global context.

Purpose of the Study:

  • Introduce and define Voronoi cohesion as a novel network measure.
  • Explore the mathematical underpinnings of Voronoi cohesion.
  • Investigate applications, particularly in community detection.

Main Methods:

  • Statistical analysis of graph-Voronoi diagrams with random cell centers.
  • Definition of node-pair Voronoi cohesion based on shared cell probability.
  • Mathematical exploration of the measure's properties.

Main Results:

  • Voronoi cohesion captures global network context, unlike other measures.
  • The measure's statistical ensemble properties correlate with large-scale network structures.
  • Identified potential and limitations for community detection.

Conclusions:

  • Voronoi cohesion is a promising metric for network analysis.
  • It provides a unique global perspective on network topology.
  • Further research can refine its application in community detection.