Network growth dynamics can be linked to evolutionary dynamics, and
specifically the quasispecies models. Below is a relevant paper with
abstract and link. We also related this work to insights of Leskovic,
Kleinberg, and Faloutsos (ref 24), which moves away from using simple
preferential attachment to explain snapshot models of power-law (and
other structured) graphs, and looks at more complex underlying growth
models that better fit the actual temporal evolution of such graphs.
- Les
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Samarth Swarup and Les Gasser, "Unifying evolutionary and network dynamics"
Physical Review E 75, 066114, 2007
Abstract
Many important real-world networks manifest small-world properties
such as scale-free degree distributions, small diameters, and
clustering. The most common model of growth for these networks is
preferential attachment, where nodes acquire new links with
probability proportional to the number of links they already have. We
show that preferential attachment is a special case of the process of
molecular evolution. We present a single-parameter model of network
growth [called "Noisy Preferential Attachment"] that unifies varieties
of preferential attachment with the quasispecies equation which
models molecular evolution, and also with the Erdős-Rényi random
graph model. We suggest some properties of evolutionary models that
might be applied to the study of networks. We also derive the form of
the degree distribution resulting from our algorithm, and we show
through simulations that the process also models aspects of network
growth. The unification allows mathematical machinery developed for
evolutionary dynamics to be applied in the study of network dynamics,
and vice versa.
DOI: 10.1103/PhysRevE.75.066114
Available at:
http://people.lis.illinois.edu/~gasser/papers/swarup-gasser-unifying-evol-netw-dyn-PhysRevE_75_066114
http://staff.vbi.vt.edu/swarup/papers/sg-unifying-evolutionary-and-network-dynamics.pdf
On 9/25/13 2:06 PM, Dawn Parker wrote:
> Hello all,
>
> A student of mine is working on a new model for her thesis, and as part of that, is doing a literature review on agent-based models of the formation of membership in groups or institutions that
> produce power-law distributions of membership. In particular, we are also interested in the agglomerative and dispersive assumptions that underlie these models.
>
> I'm happy to compile a list and report back to the mailing list.
>
> Thanks very much,
>
> Dawn
>
> Dawn Cassandra Parker
> School of Planning
> University of Waterloo
> +1-519-888-4567 x38888
> EV3 3223
> [log in to unmask] <mailto:[log in to unmask]>
> http://www.planning.uwaterloo.ca/faculty/parker/index.html
> http://wici.ca
>
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