  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.
