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The Erdos-Renyi (Erdos and Renyi, 1959) is the first ever proposed algorithm for the formation of random graphs. It selects with equal probability pairs of nodes from the graph set of nodes and connects them with a predefined probability.

To rewire, with probability (p=0.01) a 100 vertex regular graph (vertex deg=4):
>>G=erdosRenyi(40,0.01,4);

To see display the graph issue: