Critical point (network science)

In network science, a critical point is a value of average degree, which separates random networks that have a giant component from those that do not (i.e. it separates a network in a subcritical regime from one in a supercritical regime).

where the average degree is defined by the fraction of the number of edges (

[2] In a subcritical regime the network has no giant component, only small clusters.

A random network is in a subcritical regime until the average degree exceeds the critical point, that is the network is in a subcritical regime as long as

A random network is in a supercritical regime if the average degree exceeds the critical point, that is if

[3] Consider a speed dating event as an example, with the participants as the nodes of the network.

There is still no giant component in the network, the average degree is

, that is, everyone knows one other person on average, meaning that the network is at the critical point.

After the second round, the average degree of the network exceeds the critical point, and the giant component is present.

In this specific case, the average degree is