Abstract: Based on Barabási's paper in the special issue "Complex Systems and Networks" published byScience on 2009, some problems, e.g., the BA model, hierarchical networks, network dynamics, degree correlation,and network Markov chains, are discussed. Under an Markov chain framework, we provide a simple iterativemethod instead of simulation to compute network degree distribution for a class of growing networks, and thensome general criteria for judging whether a set of network generating mechanisms can ensure the existence of thesteady-stage degree distribution and whether the steady-stage degree distribution is scale-free. These results showextreme importance of strengthening basic theory and applied research for futher development of complexnetworks.