Network Growth with Preferential Attachment

based on A.-L. Barabasi & R. Albert, Emergence of Scaling in Random Networks, Science 286, 509, (1999)
The algorithm here is very simple. We start the process with a small seed network, in the example below this is a network of just two connected nodes. At each step of the algorithm a new node comes in with one or two links. With each link the node connects to one or two of the nodes in the network. The connection probability to an existing node is proportional to the degree of the target node. This way, nodes with a high degree have a higher probability of attracting incoming links which increases their degree even further. This is called preferential attachment.

As the simulation evolves, you will see that a few nodes become larger and larger as the size of the nodes is proportional to the node’s degree (the number of links it has). Note also that the age of the nodes (time since birth) is quantified by their darkness. You can see that all the highly connected nodes are mostly nodes that have been around since the beginning.