# graphs – Does every DAG have at most one “universal source”?

Suppose towards a contradiction that a DAG $$G=(V,E)$$ on $$n$$ vertices has more than one universal source and let $$u,v in V$$ be two distinct universal sources of $$G$$.

Since $$mbox{out-deg}(u)=n-1$$, and $$G$$ contains no self-loops, vertex $$u$$ has edges towards every other vertex in $$G$$. In particular $$(u,v) in E$$. As a consequence $$mbox{in-deg}(v) ge 1 > 0$$ showing that $$v$$ cannot be a universal source, yielding the sought contradiction.