In Neural network, if one node is deleted, where should other nodes be connected?
Whether you are actually removing the nodes or simply deactivating them, more or less the same concept would apply. The idea is called Dropout and is employed to inhibit the tendency to overfit. Suppose you're removing a node from the $i^{th}$ layer which has $n_i$ nodes. Removing it will not only involve removing the connections from the previous layers (${n_{i-1}}$ connections) but also removing the connections from the removed node to the next layer ($n_{i+1}$ connections) which would  essentially remove $n_{i-1}+n_{i+1}$ connections.
It would be much better to simply set the weights and biases to $0$. Here's the math behind the idea and you can find one possible implementation here.