Local Open Scope nat.
(** * Properties of subgraphs and degrees *)
(** ** Subgraph predicate [g'] is a subgraph of [g] if: - the vertex set of [g'] is a subset of the vertex set of [g] - the adjacency set of every [v] in [g'] is a subset of adjacency set of every [v] in [g] *)
Definition is_subgraph (g' g : graph) :=
S.Subset (nodes g') (nodes g) /\ forall v, S.Subset (adj g' v) (adj g v).

(** ** Subgraph relation is reflexive *)
Lemma subgraph_refl : forall g, is_subgraph g g.