Given an undirected graph $G = (V,E)$, the first Betti number of G is $|E| - |V| + k$, where $k$ is the number of connected components of $G$.
I was thinking what is the case for a directed graph $G$. Is it analogous, and the Betti number equals to the minimal number of feedback arc set (https://en.m.wikipedia.org/wiki/Feedback_arc_set)?
2026-02-23 02:09:04.1771812544
The first Betti Number of a directed graph
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