= Barabási-Albert model
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{wiki=Barabási–Albert_model}
The <Barabási-Albert model> constructs a growing <random graph> by <preferential attachment>. Starting from a suitable seed, each new vertex brings $m$ edges and selects existing endpoints with probability proportional to their current <degrees>. A convention for sampling distinct endpoints must be specified.<Emergence of scaling in random networks by Albert-László Barabási and Réka Albert>[growth and preferential-attachment rules]{ref}
Older high-degree vertices tend to attract more edges. In the standard large-graph limit, the degree distribution has a tail proportional to $k^{-3}$, unlike the sharply concentrated degrees of a basic <Erdős-Rényi model>. Both growth and the attachment rule matter. The model supplies a mechanism for hubs; observing a heavy degree tail alone does not establish that this mechanism generated the data.
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