We show how premagic capacity induces a Premagic Equilibrium (PE) with uniform congestion, and, under two additional axioms, Steady Link Characteristics (SLC) and Identical Path Link Counts (IPLC), forces the coincidence of Wardrop’s User Equilibrium (UE) and the System Optimum (SO): UE \(=\) SO \(=\) PE. This condition leads to a uniform distribution of congestion across all links. To measure distance to this ideal, we introduce the VarPi efficiency index \(\varpi =\bar g/\xi \) (capacity-weighted average congestion over peak congestion), and from it derive the Network Flow Identity (NFI), \(\kappa =\tilde c\,\varpi \,\xi \) , linking total flow, total capacity, and congestion. NFI yields a compact family of comparative-statics laws that clarify policy trade-offs (capacity, efficiency, congestion caps). We discuss applicability, limitations, and small numerical illustrations.