  In an attempt to better understand structural benefits and generalization
power of deep neural networks, we firstly present a novel graph theoretical
formulation of neural network models, including fully connected, residual
network (ResNet) and densely connected networks (DenseNet). Secondly, we extend
the error analysis of the population risk for two layer network
\cite{ew2019prioriTwo} and ResNet \cite{e2019prioriRes} to DenseNet, and show
further that for neural networks satisfying certain mild conditions, similar
estimates can be obtained. These estimates are a priori in nature since they
depend sorely on the information prior to the training process, in particular,
the bounds for the estimation errors are independent of the input dimension.
