Merging of nodes

If the graph is oriented and if its (full) incidence matrix A is written then a straightforward variant of the algorithm is possible  

By the summation of rows over n e in A get row n,. The rows h = 1, —, H) form matrix A° deleting the zero columns gives matrix A, the (full) incidence matrix of G. 

Observe finally that if the original G was connected then a fortiori the reduced graph G is connected. [Indeed, a path between any two nodes and of G can be obtained by merging on a path between some e N, and 

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Let us apply the operation merging of nodes to each subset N, of nodes of our graph G. Let G be the reduced graph obtained in this manner. Thus with... 

When we calculate the risk for an accident scenario, we sort of merge several nodes fiom right to the left. We first sum the consequence contribution from each branch and multiply with the transformed probability measure, i.e., foramerging node i, the expected consequence is given by... 

Recall that a connected component can also consist of one (isolated) node, with empty subset of incident arcs. Having merged the nodes of each N,j in G we have the reduced graph G see Fig. 3-7. The K nodes of G correspond uniquely to the K subsets N, of N. By the graph reduction (merging), we have deleted all the arcs j e J°, and some arcs j g J in addition (subset J c J ). The arc set of G , denoted by J, consists of the remaining (not deleted) arcs j e J. Thus J"" is partitioned... 

The partition of a heat exchanger (as technological unit) into two nodes (8.3.32) has been motivated by separate (generally multicomponent) mass balances of the cold and hot sides. On the other hand, it can happen that we are not interested in the (unknown) heat transfer rates. Then the latter can be eliminated by merging the nodes (8.3.32). Let us first partition the set E of net energy streams... 

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