A discussion of Barabási–Albert’s 1999 paper

Although the scale invariance is a main feature of growing networks, evidence from a few modelled networks show that the finite-size effect of network at a fixed time t cannot be ignored. We propose a concept of time-dependent scale-free networks, and prove the criteria for the stability and scale-free of growing networks by the degree-growing Markov chain. Our results show the importance of rigorous theoretical analysis for the network science.