What is the official name for the ratio of edges to nodes in a connected graph?

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In my context, the nodes are code elements and the edges are "dependencies". So I am using the term "dependency density" to refer to the ratio of edges/nodes.

Is there an official term for this ratio in a connected graph?

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In a graph the edge density ratio refers to $|E|/{|V| \choose 2}$, edges over the number of possible edges. However when working with sparse graphs, where $|E| = \Theta(n)$, it is possible to work with $|E|/|V|$, to avoid having a $1/n$ factor everywhere.

So "dependency density" makes sense in your case.