Initial attractiveness

This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (June 2015) (Learn how and when to remove this message)

The initial attractiveness is a possible extension of the Barabási–Albert model (preferential attachment model). The Barabási–Albert model generates scale-free networks where the degree distribution can be described by a pure power law. However, the degree distribution of most real life networks cannot be described by a power law solely. The most common discrepancies regarding the degree distribution found in real networks are the high degree cut-off (or structural cut-off) and the low degree saturation. The inclusion of initial attractiveness in the Barabási–Albert model addresses the low-degree saturation phenomenon.

Intuitively, it also makes sense since when moving to a new city you can still make new connections even though you don't know anyone. But in the Barabási–Albert model a node that has degree zero has probability 0 of garnering new connections. With initial attractiveness you always have a residual "attractiveness" irrespective of how many connections you already have.