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I need to create a matrix which constraints merging opportunities (presented in a integer vector). The merging opportunities are defined by adjacent nodes (i.e. connected by an edge) in an undirected network.

As an example, consider this undirected graph:

D

¦

A --- B-------

¦ .......¦.........¦

C----E------F

Starting from node A, I could merge B C and D. If B is part, F and E could be part as well. If C is part, E could be part. Moreover, I could merge all of them, or none of them. This is valid for all the possible starting node.

The matrix (or set of matrices) should be included in a constraint that limits a merging vector. As an example, a vector [A,B,0,0,E,0] should be allowed, while a vector [A,0,0,0,E,F] not, since it is not a contiguous space. Unfortunately, I am still not able to create a matrix with n columns that describes this merging possibilities.

Considering n nodes, it is possible to create n different matrices defining n different directed network (each starting from a different node). Unfortunately, this creates problems since not all the merging possibilities are allowed.

I even though to pre-create all the merging possibilities, but then the problem becomes too complex.

Thank you!

Nico
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  • Have you considered [Adjacency Matrix](https://en.wikipedia.org/wiki/Adjacency_matrix) – Francesco De Lisi Aug 05 '15 at 13:29
  • @Nico Can you please elaborate on [A,B,0,0,E,0] and [A,0,0,0,E,F]. – Sumeet Aug 05 '15 at 14:07
  • @FDL, thank you for your suggestion... I considered Adjacency matrix but as it is, it cannot be used as constraint (if multiplied by the vector of possible merger is not working as desired). I tried to modify it but unsuccessfully. – Nico Aug 05 '15 at 15:15
  • @Sumeet - They are two examples of the possible merging vectors (note that they are produced by another model). They are binary vectors [A,B,0,0,E,0] is [1,1,0,0,1,0] and show a merger between A B and E. This vector has to be constraint with respect to the graph as explained above. – Nico Aug 05 '15 at 15:17

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