Switching graphs and Hadamard matrices

Local operations of combinatorial structures (graphs, Hadamard matrices, codes, designs) that maintain the basic parameters unaltered, have been widely used in the literature under the name of switching. We show an equivalence between two switching methods to construct inequivalent Hadamard matrices, which were proposed by Orrick in 2008, and the switching method for constructing cospectral graphs which was introduced by Godsil and McKay in 1982.