Network Motif Detection — Triangle Census

Counting triangles and higher-order structures in random vs. real networks

Network motifs are recurring subgraph patterns that appear more frequently than in random null models. Triangles (3-cliques) measure clustering and transitivity. The clustering coefficient C = (triangles × 6)/(triads) quantifies this. Scale-free and small-world networks show dramatically higher triangle counts than Erdős–Rényi graphs with the same density.