** Graph Notations**

Let * (S, Γ) * be a graph and * b ∈ S * be a node.

* Γ b = { x ∈ S | (b, x) ∈ Γ } *

are the nodes that are * immediate successors* of * b * .

* Γ ^{+} b = { x ∈ S | (b, x) ∈ Γ^{+} } *

are the nodes that are

* Γ ^{-1} b = { x ∈ S | (x, b) ∈ Γ } *

are the nodes that are

Let * A ⊂ S * be a subset of the set of nodes * S *.

* Γ A = { y ∈ S | (x, y) ∈ Γ
∧ x ∈ A } *

is the set of nodes that are * immediate successors* of nodes in * A * .

* Γ ^{-1} A = { x ∈ S | (x, y) ∈ Γ
∧ y ∈ A } *

is the set of nodes that are

We say * (A, Γ _{A}) * is a

is the set of transitions within the subgraph.