  Reliable functioning of supply and transport networks fundamentally support
many non-equilibrium dynamical systems, from biological organisms and
ecosystems to human-made water, gas, heat, electricity and traffic networks.
Strengthening an edge of such a network lowers its resistance opposing a flow
and intuitively improves the robustness of the system's function. If, in
contrast, it deteriorate operation by overloading other edges, the
counterintuitive phenomenon of \emph{Braess' paradox} emerges. How to predict
which edges enhancements may trigger Braess' paradox remains unknown to date.
To approximately locate and intuitively understand such Braessian edges, we
here present a differential perspective on how enhancing any edge impacts
network-wide flow patterns. First, we exactly map the prediction problem to a
dual problem of electrostatic dipole currents on networks such that
simultaneously finding \textit{all} Braessian edges is equivalent to finding
the currents in the resistor network resulting from a constant current across
one edge. Second, we propose a simple approximate criterion -- rerouting
alignment -- to efficiently predict Braessian edges, thereby providing an
intuitive topological understanding of the phenomenon. Finally, we show how to
intentionally weaken Braessian edges to mitigate network overload, with
beneficial consequences for network functionality.
