  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 to these networks and are incorporated in the
Barab\'asi-Albert (BA) model. We provide an alternative model using a randomly
stopped linking process inspired by a generalized Central Limit Theorem (CLT)
for geometric distributions with widely varying parameters. The common
characteristic of both the BA model and our randomly stopped linking model is
the mixture of widely varying geometric distributions, suggesting the critical
characteristic of scale free networks is high variance, not growth or
preferential attachment. The limitation of classical random graph models is low
variance in parameters, while scale free networks are the natural, expected
result of real-world variance.
