Node-Level Subgraph Frequency

Definition

Given a Subgraph of interest $S$, its node $v\in S$ (the anchor), and a Graph $G$, the node-level frequency is defined as the number of nodes $u\in G$ for which some Subgraph $G^{\prime }\subset G$ is isomorphic to a specific Subgraph pattern $G^{\prime }\cong S$ and the isomorphism maps node $u\in G$ to $v\in S$.

$F_G(S,v)=|\{u\in V(G)|\exists G^{\prime }\subset G\text{s.t.}{G}^{\prime }\cong S\wedge f(u)=v\}|$ where $\cong$ means isomorphic, $f$ is an isomorphism, and $V(G)$ is the set of vertices in Graph $G$.