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**TRANSFORM>MULTIPLEX**

**PURPOSE **Constructs a multiplex graph from a multirelational graph.

**DESCRIPTION **Technically if G(V,{Ri}) is a multirelational graph with vertex set V and relations {Ri}, i e I. If v and w are two vertices of G then the bundle of relations connecting v to w, Bvw, is defined as Bvw = {Ri: vRiw}. Let Mk be the set of all bundles. The multiplex graph is the valued graph with valued adjacency matrix Xi,j = k where k is the Mk bundle of relations connecting i to j. Non technically the algorithm determines how many different distinct patterns of relations (the bundles) link any pair of vertices and assigns each of these a numerical label. The arcs in the output multiplex graph are then labeled with these identifying numbers.

**PARAMETERS**

* ***Input dataset:**

Name of file that contains multirelational binary network data. Valued data are automatically converted to multirelational binary data using a technique identical to Multigraph. Data type: Digraph. Multirelational.

* ***Include transpose(s) in the multiplexing*** *(Default = No).

For non-symmetric data the transposes can be automatically added as additional relations.

* ***Convert data to geodesic distances*** *(Default = No)

Option to convert each relation in dataset to geodesic distances.

** Output dataset*** *(Default = 'Multiplex')

Output file that will contain multiplex graph.

**LOG FILE **Multiplex graph adjacency matrix.

**TIMING** Exponential.

**COMMENTS **In the worst case, the timing for the algorithm is exponential. The timing depends on the number of possible bundles; up to 2 to the power N bundles can occur when there are N different relations.

**REFERENCES** None.