= Solution
For the \b[<Barabási-Albert model>], choose a connected seed <graph> on $m_0$ <vertices>, the number $m\leq m_0$ of new <edges> per added <vertex>, and a final size $n$. A complete seed with $m_0\geq2$ suffices. Add one <vertex> at a time, attaching it to $m$ distinct existing <vertices> selected with weights proportional to their current <vertex degrees>. Exclude duplicate <edges> and <self-loops>.
Increasing $n$ creates a larger network and permits older hubs to grow. Increasing $m$ makes the <graph> denser, with asymptotic average <vertex degree> $2m$, and tends to shorten <graph distances>. The seed affects early structure and the oldest hubs; standard linear <preferential attachment> gives a robust large-size tail exponent.
Its asymptotic <degree distribution> is $P(k)\propto k^{-3}$, so \b[it is a <scale-free network>]. Hubs produce short <average shortest path length>, but elevated <clustering coefficients> are not automatic: $m=1$ with a tree seed gives a triangle-free <tree>, and clustering decreases with size in the standard model. \b[The strict clustered <small-world network> property is therefore not guaranteed.]<Emergence of scaling in random networks by Albert-László Barabási and Réka Albert>[pp. 510–511, growth, attachment and degree exponent]{ref}
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