King [preceding Comment, Phys. Rev. E 70, 058101 (2004)] points out biases in one of the two common algorithms for generating simple random graphs—the matching, or stub-pairing, algorithm. We clarify that in our simulations of simple graphs we used a different algorithm, the Markov-chain Monte Carlo switching algorithm, which is more uniform. As for multigraphs, the stub-pairing algorithm indeed samples uniformly configurations rather than multigraphs, as King points out, and thus is relevant for our model, which pertains to configurations. Finally, we demonstrate that the algorithm we used to generate families of random networks with scale-free out-degree and compact in-degree does not result in noticeable biases.