Comment on "Abrupt transition in the structural formation of interconnected networks", F. Radicchi and A. Arenas, Nature Phys. 9, 717 (2013)

A recent paper [F. Radicchi and A. Arenas, Nature Phys. 9, 717 (2013)] presented the finding of an abrupt transition in the structure of interconnected networks. This transition was said to be generic and to occur even in networks of finite size. Furthermore, it was remarked that this singular behaviour could be understood in the spirit of a first-order phase transition. We show here that the generic singularity found in that paper is a trivial consequence of the reducibility of the "supra-Laplacian" operator studied. The singular changes observed are therefore not related to any collective abrupt structural transformation in the interconnected networks.