Certain two-terminal devices exhibiting the finger-prints of memristive behavior offer the possibility to mimic the dynamics of biological synapses with a higher level of accuracy as compared to their current electronic realizations. It has been recently shown that neural networks with memristive synapses may exhibit distinct synchronization properties over equivalent diffusively-coupled systems. Applying concepts from the contraction mapping theory, this paper derives analytical conditions for the emergence of synchronization in a memristive neural network of Hindmarsh-Rose neurons. The results reveal the crucial impact the initial memristor state has on the development of synchronous oscillations in the network.