  Many complex systems--from social and communication networks to biological
networks and the Internet--are thought to exhibit scale-free structure.
However, prevailing explanations rely on the constant addition of new nodes, an
assumption that fails dramatically in some real-world settings. Here, we
propose a model in which nodes are allowed to die, and their connections
rearrange under a mixture of preferential and random attachment. With these
simple dynamics, we show that networks self-organize towards scale-free
structure, with a power-law exponent $\gamma = 1 + \frac{1}{p}$ that depends
only on the proportion $p$ of preferential (rather than random) attachment.
Applying our model to several real networks, we infer $p$ directly from data,
and predict the relationship between network size and degree heterogeneity.
Together, these results establish that realistic scale-free structure can
emerge naturally in networks of constant size and density, with broad
implications for the structure and function of complex systems.
