Network Flow

Junction Rule: At each junction or node, the flow into that junction must equal the flow out of that junction

Using the junction rule at each node:

Rearranging each of the above gives:

Then, reducing to RREF

We find that

A negative solution for a variable means the current is flowing in the other direction.

We see that . There may be more restrictions on . For example, if the flows in the above network represent the number of automobiles moving between ## junctions, then we require the variables to be integers.