What is the difference between a simple graph and a complete graph?

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I might be having a brain fart here but from these two definitions, I actually can't tell the difference between a complete graph and a simple graph.

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2 Answers

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Every complete graph is also a simple graph. However, between any two distinct vertices of a complete graph, there is always exactly one edge; between any two distinct vertices of a simple graph, there is always at most one edge.

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A simple graph is a graph that does not contain any loops or parallel edges. So, the vertex $u$ is not adjacent to itself and if the vertex $u$ is adjacent to the vertex $v$, then there exists only one edge $uv$. A complete graph of order $n$ is a simple graph where every vertex has degree $n-1$. In other words, every vertex in a complete graph is adjacent to every other vertex.

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