Growing networks with two vertex types

Growing networks are introduced in which the vertices are allocated one of two possible growth rates; type A with probability p(t), or type B with probability 1−p(t). We investigate the networks using rate equations to obtain their degree distributions. In the first model (I), the network is constructed by connecting an arriving vertex to either a type A vertex of degree k with rate μk, where μ 0, or to a type B vertex of degree k with rate k. We study several p(t), starting with p(t) as a constant and then considering networks where p(t) depends on network parameters that change with time. We find the degree distributions to be power laws with exponents mostly in the range 2 γ 3. In the second model (II), the network is constructed in the same way but with growth rate k for type A vertices and 1 for type B vertices. We analyse the case p(t)=c, where 0 c 1 is a constant, and again find a power-law degree distribution with an exponent 2 γ 3.