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[wiki]In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other.

I support this : regular graph should be simple graph .

But another link is doubtful for me.

Please clarify this :

Is it necessary for a regular graph to be simple graph also ?

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The WIKI definition is not very good. The standard definition is, that every vertex must have the same degree. For simple graphs this coincides with "every vertex has the same number of neighbors", but for multigraphs and graphs with loops the two definitions are not equivalent.

So, no, a regular graph need not be simple.

However, you need to take care of the context you are in. Often there is an implicit or explicit assumption that all graphs are simple.

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  • $\begingroup$ Thanks for clarification . :) $\endgroup$ – 1 0 Nov 5 '15 at 6:22

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