On General Laws of Complex Networks

By introducing and analyzing a renormalization procedure, Song et al. [1] draw the conclusion that many complex networks exhibit self-repeating patterns on all length scales. First, we aim to demonstrate that the aforementioned conclusion is inadequately justified, mainly because their equation (7) on the invariance of degree distribution under renormalization does not hold in general. Secondly, Barabási and Albert [2] find that many large networks exhibit a scale-free power-law distribution of vertex degrees. They show this common feature to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to those that are already well connected. We show that when vertex degrees of large networks follow a scale-free power-law distribution with the exponent γ ≥ 2, the number of degree-1 vertices, when nonzero, is of the same order as the network size N and that the average degree is of order le...

• Type: Conference
• Year: 2009
• Where: COMPLEX
• Authors: Wenjun Xiao, Limin Peng, Behrooz Parhami
• Keywords: COMPLEX 2009, Large Networks, Scale-free Power-law Distribution, Theoretical Computer Science, Vertex Degrees