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If G = (V, E) be a non-directed graph with vertices V = {V_{1}, V_{2},…V_{n}} then

n ∑ i=1 deg(V_{i}) = 2|E|

If G = (V, E) be a directed graph with vertices V = {V_{1}, V_{2},…V_{n}}, then

n ∑ i=1 deg^{+}(V_{i}) = |E| = n ∑ i=1 deg^{−}(V_{i})

In any non-directed graph, the number of vertices with Odd degree is Even.

In a non-directed graph, if the degree of each vertex is k, then

k|V| = 2|E|

In a non-directed graph, if the degree of each vertex is at least k, then

k|V| = 2|E|

In a non-directed graph, if the degree of each vertex is at most k, then

k|V| = 2|E|

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