Why the definition of a subgraph is the way it is?

Graph with five vertices
E ⊆ {(x,y) | (x,y) ∈ V x V} 
A graph G'=(V', E') is a subgraph of another graph G=(V, E) iff
V'⊆ V and
E'⊆ E ∧ ((v1, v2) ∈ E' → v1, v2 ∈ V').
Graph G is equivalent to (V, E). Then subgraph G' is equivalent to (V', E') where V' is subset of V 
E' is subset of E but
for each edge (e) in E': end points of edge e must exist in V'
A graph and its subgraph
V' x V' = { (1, 1), (1, 2), (1, 3),
(2, 1), (2, 2), (2, 3),
(3, 1), (3, 2), (3, 3)
}
A subgraph where end points of edge (e) do not exist in V’

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Abhijeet Rai

Abhijeet Rai

Hi, I am Abhijeet. I believe everyone has a story to tell. Come, let’s chit- chat. We might end up discussing programming, history, or life. Who knows!