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splinter89 committed Jan 2, 2019
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Random power-law graphs on $n$ vertices can be defined in different ways.
One model we study describes graphs where the expected number of vertices
of degree $x$ is proportional to a power law $x^{-\beta}$, for constant $\beta>0$.
of degree $x$ is proportional to a power law $1/x^\beta$, for constant $\beta>0$.
In another model, the exact degree sequence follows the power-law distribution
and each vertex $i$ has degree $pn/i^{-\beta}$, for $0<p\leq 1$ and $\beta\geq 0$.
and each vertex $i$ has degree $pn/i^\beta$, for $0<p\leq 1$ and $\beta\geq 0$.

We show that for these models, power-law graphs contain
``large'' edge and vertex expanders.
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