ButterflyGraph[n] returns the -dimensional butterfly graph, a directed graph whose vertices are pairs , where is a binary string of length and is an integer in the range 0 through and whose edges go from vertex to , if is identical to w in all bits with the possible exception of the  bit. Here bits are counted left to right. An option VertexLabel, with default setting False, is allowed. When this option is set to True, vertices are labeled with strings . |