[8] A flow graph is more general than a directed network, in that the edges may be associated with gains, branch gains or transmittances, or even functions of the Laplace operator s, in which case they are called transfer functions.
[9] "The algebraic theory of matrices can be brought to bear on graph theory to obtain results elegantly", and conversely, graph-theoretic approaches based upon flow graphs are used for the solution of linear algebraic equations.
[10] An example of a flow graph connected to some starting equations is presented.
Look at the arrows incoming to this node (colored green for emphasis) and the weights attached to them.
For example: Using the diagram and summing the incident branches into x1 this equation is seen to be satisfied.