  We study a model for coupled networks introduced recently by Buldyrev et al.,
Nature 464, 1025 (2010), where each node has to be connected to others via two
types of links to be viable. Removing a critical fraction of nodes leads to a
percolation transition that has been claimed to be more abrupt than that for
uncoupled networks. Indeed, it was found to be discontinuous in all cases
studied. Using an efficient new algorithm we verify that the transition is
discontinuous for coupled Erdos-Renyi networks, but find it to be continuous
for fully interdependent diluted lattices. In 2 and 3 dimension, the order
parameter exponent $\beta$ is larger than in ordinary percolation, showing that
the transition is less sharp, i.e. further from discontinuity, than for
isolated networks. Possible consequences for spatially embedded networks are
discussed.
