Random processes with high variance produce scale free networks

Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms leading these incorporated in Barabási–Albert (BA) model (Barabási, 2009 [1]). We provide an alternative using a randomly stopped linking process inspired generalized Central Limit Theorem (CLT) for geometric widely varying parameters. The common characteristic of both BA our is mixture distributions, suggesting critical free high variance, not or preferential attachment. limitation models low variance parameters, while natural, expected result real-world variance.