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

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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 ``rich-get-richer'' condition we obtain networks whose statistical properties are scale-free. Assigning a quenched fitness value xᵢ 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 ``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.