Krapivsky-redner modification of nonlinear barabásialbert networks

Abstract EN

In growing Barabási-Albert (BA) networks, a new node randomly selects an existing target node and attaches to it randomly with a probability r proportional to the number k of neighbors already attached to the target node.

Krapivsky and Redner use, also for different networks: "a new node randomly selects an existing target node, but attaches to a random neighbor of this target." In nonlinear BA networks, r is made proportional to kα with α = 1 for the standard BA case.

We simulate here nonlinear BarabásiAlbert-Krapivsky-Redner (BAKR) networks, where r is applied to the selection of the target, not to the selection of the target neighbor.

We use undirected Barabási-Albert networks.

For the maximum number kmax of neighbors we find little effect from α, while the distribution n(k) of the number of neighbors has a normal power law and there is no gap or strong peak in the number of neighbors k(i).

All this contradicts our earlier simulations without redirection.