Node degree distribution

Random networks versus scale-free power-law networks

scale-free network - node degree distribution - power law

Node degree

The degree of a node in a network is the number of links to other nodes, or simply the number of contacts in a social network.
Left: In traditional random networks most nodes have a medium node degree. The degrees of all nodes are distributed around the average.
Right: Real networks often show a skewed node-degree distribution in which most nodes have only few links but, by contrast, there exist some nodes which are extremely linked. This heavy tailed distribution is known as power-law or scale-free distribution.

It should be noted that scale-free power-law node-degree distributions are not an universal characteristics of all real networks. It typically can be observed on sparsely connected networks. But more densely connected networks, by contrast, show an increasing divergence from power-law.

Further reading

→ The highly connected society
→ A similarity model for dense networks
→ (main page)

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Matthias Scholz