  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, a vertex $i$ is assigned a fitness $x_i$, drawn from a given probability
distribution function $f(x)$. During network evolution, with rate $p$ we add a
vertex $j$ of fitness $x_j$ and connect to an existing vertex $i$ of fitness
$x_i$ selected preferentially to a linking probability function $g(x_i,x_j)$
which depends on the fitnesses of the two vertices involved and, with rate
$1-p$ we create an edge between two already existed vertices with fitnesses
$x_i$ and $x_j$, with a probability also preferential to the connection
function $g(x_i,x_j)$. For the proper choice of $g$, the resulting networks
have generalized power laws, irrespective of the fitness distribution of
vertices.
