Scale-free network model of node and connection diversity.

A network model with node and connection diversity is proposed in this paper. Distinctly from to other models whose nodes and connections are represented by identical simple points and lines, we investigate inhomogeneous networks with two kinds of sites and link by growth of preferential attachment. Scale-free networks with varied centralizations and exponents (ranging from 2.0 to theoretically infinity) are obtained, and the influences of the relative ratio of the two kinds of sites p, the number of links connected from each site m, and initial attractiveness delta are studied. A mean-field theory that agrees well with our numerical results was proposed and analyzed. The theory gives the analytical scaling exponent of the form gamma=2+p+delta/m-delta(1-p)/(mp+m+delta).