While we prove that the DQ-CADMM either converges or cycles in Theorem 4, it is noted that all the numerical examples reach convergence results. Indeed, the proposed deterministic algorithms converge in most cases, as shown by the following simulation. With the same simulation setting, where p = 1 is chosen for all cases, we consider star graph which has the smallest average degree, randomly generated graph that has intermediate average degree, and complete graph that has the largest average degree for connected networks with N nodes. The result is given in the paper, where y-axis represents the number of cyclic cases in 104 trials. Clearly, the DQ-CADMM and the PQDQ-CADMM with p = 1 converge in most cases, particularly with large networks. Besides, it is worth mentioning that our subsequent work investigates the effect of p on the algorithm's performance and proposes a decreasing strategy which accelerates the algorithm under certain consensus accuracy constraint.