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Triangle Counting and Centrality

Chapter 8

Interactive Notebook

Summary

This chapter explores triangle structures and node importance in graphs:

  • Triangles in Graphs - Three mutually connected nodes forming the fundamental building block for graph analysis
  • Algebraic Triangle Counting - Using matrix operations (A² ⊙ A) to efficiently count triangles
  • Triangle Counting Algorithms - Different approaches with various performance characteristics
  • Centrality Measures - Ranking node importance based on structural position in the graph
  • Triangle-based Centrality - Determining node importance by counting triangles around each node
  • Applications - Social network analysis, community detection, and graph clustering