# Order, Size and Degree

Graphs have an order equal to the number of vertices that they contain.

The size of a graph is equal to the number of edges.

Complete graphs have the maximum size for a given order, without loops. For a graph of order $n$ the maximum size will be $\dfrac {n}{2}\left( n-1\right)$.

The degree of a vertex is equal to the number of edges that enter or leave it.

The maximum vertex degree for a given order, $n$, of graph without loops, is $n-1$.

The sum of vertex degrees will be double the size of the graph as each edge has two ends. Consequently a graph cannot have an odd number of vertices with an odd degree.

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