A scale-free network is a type of network characterized by a particular property in its degree distribution. In such networks, the distribution of connections (or edges) among the nodes follows a power law, which means that a few nodes (often referred to as "hubs") have a very high number of connections, while the majority of nodes have relatively few connections.
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A scale-free network has a degree distribution with an approximately power-law tail over a meaningful range. Evidence requires degrees from enough vertices to assess that range and compare alternative tail models. Large clustering coefficients or short graph distances alone do not establish this property.