Asymptotic behavior of connecting-nearest-neighbor models for growing networks
by Dr David Juher
Abstract: Several situations can be modelled by growing networks: spread of infectious
diseases through populations, the structure of Internet and the worldwide web, citation
of papers, predator-prey relationships in an ecosystem, percolation theory, etc. At least
in a subfamily of these networks (including citation and social networks), a reasonable
assumption for the growth rules is the CNN (connecting nearest neighbor) mechanism, which
favors the creation of new links between pairs of nodes with a common neighbor. The evolution
of the network can be described by a pair of mean-field nonlinear differential equations
(A. Vazquez, "Growing networks with local rules: preferential attachment, clustering hierarchy
and degree correlations", Phys. Rev. E 67, 2003). We will analyze the asymptotic behavior of
the solutions, which differs from the one predicted by the linear reduction proposed by Vazquez.
We will contrast the predictions with the long-time behavior of an "in silico" model (a particular
case of the previous one), obtained from simulations.
For More Information: Iwan Jensen tel. 03 8344-5214 email: email@example.com