A complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge.
A tree is an undirected graph in which any two vertices are connected by exactly one path.
To me, these two types of graphs seem like some kind of opposites in terms of connectivity. I have been searching online for a graph property that reflects this difference, like Wiener index, circuit rank, strength, etc.
I couldn't find a property that measures the thing I desire: something like an averaged number that defines a node's connectivity to more than 1 node. A normalized value that should be minimum for a tree e.g. ~0 and maximum for a complete graph e.g. ~1.
Does such a measure exist in literature?