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Dynamic graphs, community detection, and Riemannian geometry.

Craig Bakker1, Mahantesh Halappanavar1, Arun Visweswara Sathanur1

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This study introduces a novel Riemannian geometry framework for dynamic community detection in evolving networks. Riemannian methods outperform linear interpolation for tracking network communities over time.

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Area of Science:

  • Network Science
  • Graph Theory
  • Computational Geometry

Background:

  • Defining communities in complex networks is crucial for understanding network structure and dynamics.
  • Dynamic community detection addresses the challenge of identifying evolving communities in time-varying graphs.
  • Existing methods often struggle with the non-Euclidean nature of graph data over time.

Purpose of the Study:

  • To present a novel framework for dynamic community detection using Riemannian geometry.
  • To enable operations like interpolation and averaging on graph snapshots within a geometric framework.
  • To compare the efficacy of Riemannian methods against traditional linear interpolation techniques.

Main Methods:

  • Development of a framework based on Riemannian geometry for graph analysis.
  • Implementation of interpolation and averaging operations on graph snapshots.
  • Comparative analysis of Riemannian methods versus entry-wise linear interpolation.

Main Results:

  • Riemannian geometry provides a more suitable approach for dynamic community detection compared to linear interpolation.
  • The proposed framework effectively handles the temporal evolution of communities in graphs.
  • Demonstrated superior performance of Riemannian methods in interpolating and averaging graph structures.

Conclusions:

  • Riemannian geometry offers a powerful mathematical foundation for dynamic community detection.
  • The developed framework shows promise for accurately tracking evolving network structures.
  • Future work will focus on extending the framework for noisy data and improving scalability.