I was trying to solve a problem to design an algorithm to determine whether a direct graph is semi-connected. Someone says it can be done by using topological sort every SCC in the graph. And SCC is guaranteed to be DAG. However, I think SCC graph must be a circle, why it is a DAG since DAG mean no circle.
In the graph theory, is a strongly connected component SCC form a DAG?
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You misunderstood the argument.
Suppose you have a graph that has points
A1 <--> A2 <--> A3 --> B1 <--> B2 --> C1 <--> C2and
A1 A2 A3,B1 B2,C1, C2are SCC.Then you treat
A1 A2 A3as a single pointA. Any node connecting to one ofA1 A2 A3is treated as connecting toA, Any node connected from one ofA1 A2 A3is treated as connected fromA. Same for merging points toB,CSo it became
A --> B --> C. It is guaranteed that this is a DAG.