What Is It?
This exploratory model is based off of Wilensky, U. (2005). NetLogo Preferential Attachment model. Wilensky’s model produces the initial network. Future Forward Institute added the functionality to decay the network.
In some networks, a few “hubs” have lots of connections, while everybody else only has a few. This model shows one way such networks can arise. This model generates these networks by a process of “preferential attachment”, in which new network members prefer to make a connection to the more popular existing members.
This model then decays the network by a process of “random removal” of nodes along with their links.
How Does It Work?
The model starts with two nodes connected by an edge.
At each step, a new node is added. A new node picks an existing node to connect to randomly, but with some bias. More specifically, a node’s chance of being selected is directly proportional to the number of connections it already has, or its “degree.” This is the mechanism which is called “preferential attachment.”
The decay function removes nodes at random from the network, including all of the links associated with that node. This demonstrates how quickly large sections of the network can collapse.
What Does It Show?
The network used in this model are often called “scale-free” or “power law” networks.
When you decay this network by random removal of nodes with their links, most of the nodes removed are likely to have few links. Consequently, the network suffers little decay. Removal of nodes with high-degree, i.e. ‘hubs’, will cause more decay to the network. Eventually the network suffers enough decay that large numbers of nodes become isolated from each other.
This is a non-linear effect, not a trend, and is unpredictable. Because nodes are removed randomly there is no way to predict when the hubs will get removed, or when the combined effect of their absence isolates most of the rest of the network. Nevertheless, the graph of the ‘Giant Component’ shows how quickly total collapse can occur.
Try It Yourself!
You can run and play with the model in realtime right here:
You can also download or fork the code from github here:
The Future Forward Institute is currently crowd-fundraising to do a complex systems model of economic transformation. To contribute see http://rockethub.com/projects/1349-understanding-today-s-economic-transformation