Partition of variables and equations

In the set J of arcs j thus of variables mj, let us assume that certain variables have been fixed as (say) m let be the corresponding set of arcs, J° = J - the remaining subset. Generally, the values m can be certain measured values, or also certain target values required when designing the plant or otherwise. Making abstraction from the way how the m have been determined, we see immediately that the set of equations (3.1.2) 

When restricting the graph G to arcs j g J , we obtain a subgraph (say) G° its reduced incidence matrix is of elements C j where n N and j g J . The subgraph is generally not connected it can even contain isolated nodes, not incident with any arc j g J°. Example  

Generally, let us partition the vector of unknown streams into subvectors 

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