Frequent Graph Mining

Years and Authors of Summarized Original Work

• 2000; Inokuchi, Washio

• 2002; Yan, Han

• 2004; Nijssen, Kok

Problem Definition

This problem is to enumerate all subgraphs appearing with frequencies not less than a threshold value in a given graph data set. Let G(V, E, L, ℓ) be a labeled graph where V is a set of vertices, E ⊆ V × V a set of edges, L a set of labels and ℓ : V ∪ E → L a labeling function. A labeled graph g(v, e, L, ℓ) is a subgraph of G(V, E, L, ℓ), i.e., g ⊑ G, if and only if a mapping f : v → V exists such that $\forall u_{i} \in v,f(u_{i}) \in V$, $\ell(u_{i}) =\ell (f(u_{i}))$, and $\forall (u_{i},u_{j}) \in e,(f(u_{i}),f(u_{j})) \in E$, ℓ(u _i , u _j ) = ℓ(f(u _i ), f(u _j )). Given a graph data set $D =\{ G_{i}\vert i = 1,\ldots ,n\}$, a support of g in D is a set of all G _i involving g in D, i.e., $D(g) =\{ G_{i}\vert g \sqsubseteq G_{i} \in D\}$. Under a given threshold frequency called a minimum support minsup > 0, g is said to be frequent, if the size of D(g) i.e....