How the vector of weights is assigned to a Neural Network Say for example, you have an artificial neural network like the one given below- 



You have set of input nodes, hidden nodes and output nodes although I have one output node in my case.

We assign weights to the connections between those nodes. So is there any pattern of assigning weights to those connections i.e. See the first connection between first input(top) node and first hidden(top) node. So is it that the connection is assigned first value from the vector of weights,

the second the connection between first(top) input and second(second from top) hidden node is assigned second value from the vector of weights .

In short, what am I asking is that - Is there any correspondence between the position of the weight in the vector of weights and the connections in the structure. Is there any matrix that is assigned?
Yes, I am asking about Backpropagation algorithm. I want to understand how the weights get assigned to the neural network. If we want to assign a weight matrix to the neural network, how will we assign it?