Scale-free Networks without Growth or Preferential Attachment: Good get Richer

Abstract

A new mechanism leading to scale-free networks is proposed in this letter. It is shown that in many cases of interest, the connectivity power-law behavior is neither related to dynamical properties nor to preferential attachment. Instead, we show that without increasing the number of vertices in time and without applying the so called {\it ``rich-get-richer''} condition we obtain networks whose statistical properties are scale-free. Assigning a quenched fitness value $x_i$ to every vertex, and drawing links among vertices with a probability depending on the fitnesses of the two involved sites, gives rise to what we call a {\it ``good-get-richer''} mechanism, in which sites with larger fitness are more likely to become hubs (i.e., to be highly connected). This procedure generates power-law behaviors for various fitness distributions and attaching rules.