  For quantum field theories that flow between ultraviolet and infrared fixed
points, central functions, defined from two-point correlators of the stress
tensor and conserved currents, interpolate between central charges of the UV
and IR critical theories. We develop techniques that allow one to calculate the
flows of the central charges and that of the Euler trace anomaly coefficient in
a general N=1 supersymmetric gauge theory. Exact, explicit formulas for
$SU(N_c)$ gauge theories in the conformal window are given and analysed. The
Euler anomaly coefficient always satisfies the inequality $% a_{UV}-a_{IR}>0$.
This is new evidence in strongly coupled theories that this quantity satisfies
a four-dimensional analogue of the $c$-theorem, supporting the idea of
irreversibility of the RG flow. Various other implications are discussed.
