Should the entry (adjacency matrix) for row = g, column = g be "2" instead of 1?
Also, should the entry (incidence matrix) for row = g, column = e11 be "2" instead of 1?
I have one lecturer saying that both entries should be "1" and another lecturer saying these two entries should have "2". This looks like it should be obvious; but, I've been given conflicting information about these entries and want to check if there is a "right" answer.
Best Answer
Consider the degree sum formula for a graph $G = (V,E)$, $$\sum_{v \in V} \text{degree} \ v = 2|E|.$$ Now take a look at the multi-graph $G = (\{1\},\{1,1\})$. We obviously get a contradiction if we work with this definition of a self-loop ($\text{degree} \ v = 1$ for edge $\{v,v\}$).