When newcomers favor the popular, how far ahead can one node get? One gray node appears per tick, and its links tend to go to nodes that already have many.
Try this Set final-nodes to 200 and press Reset (it is read only at setup). max-degree now ends around 27 to 44 instead of 18 to 26. With 2.5 times as many nodes the biggest hub grows by about half, close to the square-root growth the Barabási–Albert model predicts.
About this model Where it ends up
Barabási and Albert's growth model (Science, 1999), as in Uri Wilensky's Preferential Attachment in the NetLogo Models Library: a network grows one node at a time, and each newcomer links to existing nodes with probability proportional to their degree. Nodes that joined early keep attracting links, which gives the degree distribution a heavy tail.
Setup places final-nodes nodes at random positions, hidden, and links nodes 0 and 1. Each tick the next node appears and makes links-per-node picks among the nodes already in the network, each pick weighted by degree (degrees are updated after all of that tick's picks). Two picks can land on the same node, in which case the newcomer gets fewer links. Nodes are colored by degree, gray for 1 to 3 links, amber for 4 to 7 and orange for 8 or more. final-nodes is read only at setup and links-per-node every tick. The biggest hub is almost always one of the first half-dozen nodes.
NetLogo's version adds one link per new node, so its network is a tree, and it lays the network out with springs and plots the degree distribution. Here nodes stay where they were placed, so the board shows degree through node size and color rather than the network's shape, and there is no degree-distribution plot.
