The Braess Paradox as a Symmetry-Breaking Transition in Network Flows.

This preprint investigates the Braess paradox from a dynamical and structural perspective. The Braess paradox is a well-known phenomenon in network theory in which adding a new connection to a transportation network can paradoxically increase overall travel times. Traditional explanations focus on game-theoretic arguments based on Nash equilibria and selfish routing. This article proposes a complementary interpretation based on symmetry and dynamical stability. It argues that the Braess paradox can be understood as a symmetry-breaking transition in network flows: a previously symmetric equilibrium becomes unstable when the addition of a new link introduces a new degree of freedom. The paper introduces a heuristic conceptual parameter describing the degree of continuity of the transported flow, ranging from discrete agent-based systems such as traffic networks to strongly coupled continuous systems such as fluids and plasmas. Within this framework, the paradox is interpreted as a bifurcation phenomenon emerging when flow granularity and informational coordination exceed a critical threshold. The analysis connects this interpretation to the geometry of the Beckmann transport functional, the local loss of convexity of the transport potential, and conceptual phase diagrams describing regimes of network flow behavior. This work is part of a broader research program on the structural nature of paradoxes in science. Three preceding papers developed a general theoretical framework for understanding paradox formation and conceptual instability in scientific systems. The present article represents the first application of this framework to a concrete case study: the Braess paradox. A companion article develops the dynamical thresholds and explicit network models in greater detail.