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We give a new way to study recursive towers of curves over a finite field,defined from a bottom curve $\Cun$ and a correspondence $\Cdeux$ on $\Cun$.Inparticular, we study their asymptotic behavior. A close examination ofsingularities leads to a necessary condition for a tower to be asymptoticallygood. Then, spectral theory on a directed graph and considerations on the classof $\Cdeux$ in $\NS (\Cun \times \Cun)$ lead to the fact that, under some mildassumptions, a recursive tower which does not reach Drinfeld-Vladut boundcannot be optimal in Tsfasmann-Vladut sense. Results are applied to theBezerra-Garcia-Stichtenoth tower along the paper for illustration.

Recursive towers of curves over finite fields using graph theory