Why does one count a loop as a double in graph degree?
Rather than just as a single?
From Wikipedia:
a vertex with a loop "sees" itself as an adjacent vertex from both ends of the edge thus adding two, not one, to the degree.
Or perhaps this is just a feature of undirected graphs.
However, I wonder, what's the usefulness of counting a loop as a double in undirected graph?
A basic result of graph theory is the degree sum formula: $$\sum_{v \in V} \deg v = 2 \lvert E \rvert$$ This formula holds on loop-graphs only if we let $\deg v = 2$ for any loop $v$. For a simple example, consider the graph consisting of just one loop.