If $A$ is an edge-node incidence matrix for a directed graph, then:
- Each row has exactly one $-1$ entry and $+1$ entry
- $dim(Nul(A))$ is the number of independent loops in the directed graph
Would both of these statements be true? I'm especially unsure about the second one because I'm confused about whether an independent loop is another word for connected component. I know that the second statement would be true if we were talking about the number of connected components.