MOTIF COUNTING

Network building blocks and their frequencies

25
0.15
Triangle
0.50
Network motifs are small, recurring subgraph patterns that appear significantly more often in real networks than in random graphs — they serve as the fundamental building blocks of complex networks. The 13 connected undirected graphs on 3–4 nodes include triangles (3-cliques), paths, stars, and squares. Triangle counting via matrix multiplication (tr(A³)/6) runs in O(n^ω) where ω ≈ 2.37. The motif significance profile, introduced by Milo et al. (2002 Science), distinguishes network types: transcriptional networks are rich in feed-forward loops, while social networks are dominated by triangles reflecting transitivity.