Two evolving social network models


Journal Article

In our first model, individuals have opinions in [0, 1] d . Connections are broken at rate proportional to their length β„“, an end point is chosen at random, a new connection to a random individual is proposed. In version (i) the new edge is always accepted. In version (ii) a new connection of length β„“' is accepted with probability minβ„“/β„“', 1. Our second model is a dynamic version of preferential attachment. Edges are chosen at random for deletion, then one endpoint chosen at random connects to vertex z with probability proportional to f(d(z)), where d(z) is the degree of z, f(k) = θ(k+1)+(1-θ)(d+1), d is the average degree. In words, this is a mixture of degree-proportional, at random rewiring. The common feature of these models is that they have stationary distributions that satisfy the detailed balance condition, are given by explicit formulas. In addition, the equilibrium of the first model is closely related to long range percolation, of the second to the configuration model of random graphs. As a result, we obtain explicit results about the degree distribution, connectivity, diameter for each model.

Duke Authors

Cited Authors

  • Magura, SR; Pong, VH; Durrett, R; Sivakoff, D

Published Date

  • January 1, 2015

Published In

Volume / Issue

  • 12 / 2

Start / End Page

  • 699 - 715

International Standard Serial Number (ISSN)

  • 1980-0436

Citation Source

  • Scopus