We propose a new method for simultaneous synchronization and topology identification of a complex dynamical network that relies on the edge-agreement framework and on adaptive-control approaches by design of an auxiliary network. Our method guarantees the identification of the unknown topology and it guarantees that once the topology is identified the complex network achieves synchronization. Under our identification algorithm we are able to provide stability results for the estimation errors in the form of uniform semiglobal practical asymptotic stability. Finally, we demonstrate the effectiveness of our approach with an illustrating example.