Non-Universality in Semi-Directed Barabasi-Albert Networks

TL;DR

This paper investigates how introducing limited directedness in Barabasi-Albert networks causes the degree distribution exponent gamma to decrease from 3 to 2 as the number of links m increases, challenging the universality of gamma.

Contribution

It demonstrates that the degree distribution exponent gamma is not universal in semi-directed Barabasi-Albert networks and varies with the parameter m.

Findings

Gamma decreases from 3 to 2 as m increases.

Limited directedness affects the universality of the degree distribution.

Degree distribution exponent is dependent on network construction parameters.

Abstract

In usual scale-free networks of Barabasi-Albert type, a newly added node selects randomly m neighbors from the already existing network nodes, proportionally to the number of links these had before. Then the number N(k) of nodes with k links each decays as 1/k^gamma where gamma=3 is universal, i.e. independent of m. Now we use a limited directedness in the construction of the network, as a result of which the exponent gamma decreases from 3 to 2 for increasing m.