The average kissing number of $mathbb{R}^n$ is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in $mathbb{R}^n$. We provide an upper bound for the average kissing number based on semidefinite programming that improves previous bounds in dimensions $3, ldots, 9$. A very simple upper bound for the average kissing number is twice the kissing number; in dimensions $6, ldots, 9$ our new bound is the first to improve on this simple upper bound.
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