fivevertexscale
Fivevertexscale is a graph-theoretic descriptor that quantifies the occurrence and arrangement of five-vertex induced subgraphs within a finite simple graph. It serves as a local-structure metric that captures motif composition and diversity in the network, providing a compact summary of five-vertex patterns beyond basic degree-based measures.
The standard definition uses the set of all induced subgraphs on five vertices. For a graph G
Properties and interpretation: The vector p is invariant under graph isomorphism and reflects motif composition independent
Computation and applications: Exact counting requires enumerating all five-vertex induced subgraphs and performing isomorphism tests, which