title: Lower bound of assortativity coefficient in scale-free networks.
abstract: The degree-degree correlation is important in understanding the structural organization of a network and dynamics upon a network. Such correlation is usually measured by the assortativity coefficient r, with natural bounds r∈[-1,1]. For scale-free networks with power-law degree distribution p(k)∼k-γ, we analytically obtain the lower bound of assortativity coefficient in the limit of large network size, which is not -1 but dependent on the power-law exponent γ. This work challenges the validation of the assortativity coefficient in heterogeneous networks, suggesting that one cannot judge whether a network is positively or negatively correlated just by looking at its assortativity coefficient alone.
authors.affiliation: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China.
authors.forename: Dan
authors.identifier: 0000000227069476
authors.initials: D
authors.lastname: Yang
authors.affiliation: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China.
authors.forename: Liming
authors.initials: L
authors.lastname: Pan
authors.affiliation: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China.
authors.forename: Tao
authors.initials: T
authors.lastname: Zhou