EXPLORABLES

This explorable illustrates a network model that captures how opinion dynamics might work in a population and how clusters of uniform opinion might naturally emerge from an initially random system. The model is a variant of a model introduced by
P. Holme and M. Newman in a 2006 paper: *Nonequilibrium phase transition in the coevolution of networks and opinions*.

The model describes a network with a fixed number of nodes and links. Each node can have one opinion. Links that connect two nodes with different opinions can induce an opinion change in one of the nodes. Alternatively, a discordant link can be cut and one of the nodes rewires to another random node.

For some parameters the final state can be a uniform population in which only one opinion survives. For other parameters the population can equilibrate to a state of disconnected uniform little groups.

**Press Play** and keep on reading…

## This is how it works

Initially the system starts with 160 nodes and a every node has on average 2.5 connections. Every node is assigned one opinion from a pool of 10 different opinions classified by color.

When the model evolves one of the discordant links (connecting nodes with different opinions say node *A* and *B*) is chosen at random. Then two things can happen:

- With a
that you can chose with a slider the link is cut, one of its nodes, either**rewiring probability***A*or*B*takes it and connects to another random node in the network. - If the link isn’t cut
(with a 50% chance).**either A takes B’s opinion or vice versa**

Now, * there’s an additional twist.* When a node cuts a link it can either be open-minded and pick a friend irrespective of opinion, or the opposite, only seek like-minded nodes. You can control the

*.*

**propensity with the open-mindedness slider**## Observe this

To see a fast effect, turn the open-mindedness all the way to the left and the rewiring probability to its maximum value. In this regime nodes don’t change their opinion. Very quickly, the network should segreggate into uniform little groups.

Reset the parameters and turn the rewiring probability to its minimum value. If you wait a bit, the fluctuations in the system will yield a system in which a dominant opinion emerges and others disappear.

For intermediate values you should be able to determine a critical value for the rewiring probability beyond which the network will always seggregate into isolated groups.

## References

- P. Holme and M. E. J. Newman, Nonequilibrium phase transition in the coevolution of networks and opinions, Phys. Rev. E 74, 056108 (2006)
- R. Durrett, J. P. Gleeson, A. L. Lloyd, P. J. Mucha, F. Shi, D. Sivakoff, J. E. S. Socolar, C. Varghese, Graph fission in an evolving voter model, PNAS March 6, 109 (10) 3682-3687 (2012)

## Acknowledgements

I want to thank Pawel Romanczuk for sugggesting this explorable and pointing out the above papers.