The adaptive voter model is a conceptual and one of the most prototypical models of opinion dynamics. It was first introduced by Petter Holme and Mark Newman in 2006 and still forms the basis of many studies conducted in my current research group. It is motivated from the observation that in social networks like-minded individuals tend to cluster in groups or communities. This effect may be explained either by individuals becoming like-minded because they are connected or by individuals connecting with each other because they are like-minded. The latter is often denoted as “homophily”.

The model is comprised of a network with N (here N=50) nodes. Initially each node carries one of G (here G=8) opinions. In each time step one node i is chosen uniformly at random and one of the two following processes happen:

• Rewiring/adaptation: With probability Φ one of the edges attached to i is moved to another randomly chosen node with the same opinion as node i
• Imitation: With probability 1-Φ node i copies the opinion of one of its neighbors j

The simulation ends once there are no more links between nodes of different opinion. For low values of Φ the model converges into a state with one giant component in which all nodes hold the same opinion. At intermediate Φ the system undergoes a phase transition where the giant component vanishes and the final distribution of cluster sizes follows a power law. For large Φ the network quickly fragments and the size distribution of final clusters approximately equals the initial distribution.

Use the buttons below to control the model. The buttons “Slow” or “Fast” both start the simulation. In the “Slow” mode you should be able to follow exactly what is happening at each time step. Use the “Fast” mode to run the model into its final state. Use “Reset” to start over. The slider on the right is used to adjust the rewiring probability Φ. This can only be changed when the simulation is stopped.