  This paper addresses the problem of determining the maximum number of edges
in a unit distance graph (UDG) of $n$ vertices using computer search. An
unsolved problem of Paul Erd\H{o}s asks the maximum number of edges $u(n)$ a
UDG of $n$ vertices can have. Those UDGs that attain $u(n)$ are called
"maximally dense." In this paper, we seek to demonstrate a computer algorithm
to generate dense UDGs for vertex counts up to at least 100. Via beam search
with an added visitation metric, our algorithm finds all known maximally dense
UDGs up to isomorphism at the push of a button. In addition, for $15 < n$,
where $u(n)$ is unknown, i) the algorithm finds all previously published
densest UDGs up to isomorphism for $15 < n \le 30$, and ii) the rate of growth
of $u(n)/n$ remains similar for $30 < n$. The code and database of over 60
million UDGs found by our algorithm will be open-sourced at time of
publication.
