title: Scale-free networks with tunable degree-distribution exponents.
abstract: We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on popularity-driven and fitness-driven preferential attachments. As the network grows, a newly added node establishes m new links to existing nodes with a probability p based on popularity of the existing nodes and a probability 1-p based on fitness of the existing nodes. An explicit form of the degree distribution P(p,k) is derived within a mean field approach. For reasonably large k, P(p,k) approximately k(-gamma(p)) F(k,p), where the function F is dominated by the behavior of 1/ln (k/m) for small values of p and becomes k independent as p-->1, and gamma(p) is a model-dependent exponent. The degree distribution and the exponent gamma(p) are found to be in good agreement with results obtained by extensive numerical simulations.
authors.affiliation: Department of Physics, The Chinese University of Hong Kong, New Territories, Shatin, Hong Kong, China.
authors.forename: H Y
authors.initials: HY
authors.lastname: Lee
authors.forename: H Y
authors.initials: HY
authors.lastname: Chan
authors.forename: P M
authors.initials: PM
authors.lastname: Hui