This report documents the program and the outcomes of Dagstuhl Seminar 23422 "Graph Algorithms: Cuts, Flows, and Network Design". This seminar brought 25 leading researchers in graph algorithms together for a discussion of the recent progress and challenges in two areas: the design of fast algorithm for fundamental flow/cut problems and the design of approximation algorithms for basic network design problems. The seminar included several talks of varying lengths, a panel discussion, and an open problem session. In addition, sufficient time was set aside for research discussions and collaborations.