Summary: A Tractable Complex Network Model Based
on the Stochastic Mean-Field Model of Distance
David J. Aldous
Department of Statistics, 367 Evans Hall, University of California, Berkeley CA
Abstract. Much recent research activity has been devoted to empirical study and
theoretical models of complex networks (random graphs) possessing three qualitative
features: power-law degree distributions, local clustering, and slowly-growing diameter.
We point out a new (in this context) platform for such models the stochastic mean-
field model of distances and within this platform study a simple two-parameter
proportional attachment (or copying) model. The model is mathematically natural,
permits a wide variety of explicit calculations, has the desired three qualitative features,
and fits the complete range of degree scaling exponents and clustering parameters; in
these respects it compares favorably with existing models.
The topic of complex networks, more precisely the design and theoretical analysis
of stochastic models of large graphs which differ from the classical Erdos - R´enyi
model, has attracted intense recent attention, surveyed from a statistical physics
viewpoint in  and from a rigorous mathematical viewpoint in .
Let us frame one aspect of this topic, by analogy. In freshman statistics