Effect of fitness on mutual selection in network evolution

We propose a new mechanism leading to scale-free networks which is based on the presence of an intrinsic character of a vertex called fitness. In our model, at each vertex i a fitness xi, drawn from a given probability distribution function f(x), is assigned. During network evolution, with rate p we add a vertex j and connect to an existing vertex i of selected preferentially to a linking probability function g(xi,xj) which depends on the fitnesses of the two vertices involved and, with rate 1−p we create an edge between two already existed vertices i and j, with a probability also preferential to the connection function g(xi,xj). For the proper choice of g, the resulting networks have power-law distributions of connectivity and small-world properties, irrespective of the fitness distribution of vertices.