Growing network models
Example of a growing network model. Nodes added at each timestep is labelled by the timestep that it was added. New nodes prefer to be attached to nodes with existing connections.
For the general public (click to open and close)
Growing network models are simple models that model social settings. For example, it could model how much research papers are cited - people tend to cite papers that are already cited (preferential attachment). This effect by itself leads to winner-takes-all effects, with winners randomly chosen due to random fluctuations. We study some of the models and come up with more accurate expressions for certain limits.
Abstract (click to open and close)
Three growing network models (GNMs) are studied numerically using Monte Carlo sampling and analytically using mean-field approximation. The first is the Barabási-Albert (BA)/PurePref model, where new nodes are connected preferentially connected to existing nodes with many preexisting links. The second is the PureRand model, where there is no preference. The third is the Mixed model, where node choice probability is chosen between the two models. Apart from rederivation of known results, our original contribution is as follows. We study the node degree evolution directly instead of the steady state distribution, to find an analytic form more accurate with number of edges added per timestep, $m$. We confirm the results with numerics.
