aging.prefatt.game: Generate an evolving random graph with preferential attachment and aging

Description

This function creates a random graph by simulation its evolution. Each time a new vertex is added it creates a number of links to old vertices and the probability that an old vertex is cited depends on its in-degree (preferential attachment) and age.

Usage

aging.prefatt.game(n, m=1, aging.type="exponential", params=list(), ...)

Arguments

The number of vertices in the graph.

The number of edges each new vertex creates (except the very first vertex.

aging.type

Character string, the type of the function giving probability that an old vertex is cited depending on its age. See details below.

params

Named list, this gives the parameters of the aging function selected by the aging.type argument. See details below.

...

Additional arguments, these are passed to the graph constructor.

Value

A new graph.

Details

This is discrete time step model, in each time step a new vertex is added to the network. The new vertex cites a number (parameter m) of other vertices. The probability that a vertex is cited is proportional to the product of the in-degree of the node plus one and the so-called aging function (aging.type arguments).

The exponential aging function decreases exponetially with age with exponent aging.exp, its only parameter.

The powerlaw aging function decreases as a power law with age, the exponent is given by the aging.exp parameter.

Examples

Run this code

g <- aging.prefatt.game(100, aging.type="exponential",
     params=list(aging.exp=1/100))
g2 <- aging.prefatt.game(100, aging.type="powerlaw",
     params=list(aging.exp=1))