A single new connection can dramatically enhance the size of a network — no matter whether this connection represents an additional link in the Internet, a new acquaintance within a circle of friends or a connection between two nerve cells in the brain.
The results, which are published inNature Physics, were part of a theoretical study carried out by researchers from the Max Planck Institute for Dynamics and Self-Organization (MPIDS), the Bernstein Center for Computational Neuroscience Göttingen and the University Göttingen. This study mathematically describes for the first time the influence of single additional links in a network.
Imagine the following scenario: In your sports team you get to know a new player and arrange to go out and see a movie on the next weekend. The new team member brings along three friends — and suddenly by adding one new contact, your own circle of friends has grown by four people. Growth processes of this sort occur in many networks: Neurons in the brain constantly establish new connections, websites link to each other and a person travelling infected with influenza creates a network of infected places with each intermediate stop. From a scientist’s point of view, such growth processes are still poorly understood: How does a network change when single links are added? How quickly does a network grow in this way?
To answer these questions, the scientists from Göttingen tracked the growth of networks link by link. A new connection, however, can not only add one new element. It can also merge two networks (as in the example in the sports team above). The researchers focused on a special form of network growth that introduces a form of competition between possible links: If several new connections are possible, only the one connection is created: the one that results in the smallest new network.