Distribution of number of neighbors on semi-directed Barab'asi-Albert networks with many initial neighbors

Abstract EN

On directed and undirected Barba'asi-Albert networks, when a new node has selected m old nodes as neighbors, then the m old nodes are added to the Kert'esz list, and the new node is also added m times to that list.

These connections are made with m randomly selected elements of that list.

If one adds to the list the m old nodes, plus only once and not m times the new node, one gets a semi-directed network (SDBA).

Now we check the number of neighbors on two versions (SDBA1 and SDBA2) for semi-directed Barba'asi-Albert networks.

We found that SDBA2 does not give proper power laws for large m but it does so for small m, whereas SDBA1 gives proper power laws for large and small m.

The resulting exponents vary with m.