page_title: Scale-free network
section_title: Characteristics
hierarchical_section_title: Scale-free network / Characteristics
context_page_description: A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P of nodes in the network having k connections to other nodes goes for large values of k as
  where is a parameter whose value is typically in the range 2 < < 3, although occasionally it may lie outside these bounds.
  Many networks have been reported to be scale-free, although statistical analysis has refuted many of these claims and seriously questioned others. Preferential attachment and the fitness model have been proposed as mechanisms to explain conjectured power law degree distributions in real networks.
context_section_description: The most notable characteristic in a scale-free network is the relative commonness of vertices with a degree that greatly exceeds the average. The highest-degree nodes are often called "hubs", and are thought to serve specific purposes in their networks, although this depends greatly on the domain.
caption: Random network (a) and scale-free network (b). In the scale-free network, the larger hubs are highlighted.
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