graphtopoorder - Perform topological sort of directed acyclic graph

Syntax

Arguments

G	N-by-N sparse matrix that represents a directed acyclic graph. Nonzero entries in matrix G indicate the presence of an edge.

Description

Tip   For introductory information on graph theory functions, see Graph Theory Functions in the Bioinformatics Toolbox User's Guide.

order = graphtopoorder(G) returns an index vector with the order of the nodes sorted topologically. In topological order, an edge can exist between a source node u and a destination node v, if and only if u appears before v in the vector order. G is an N-by-N sparse matrix that represents a directed acyclic graph (DAG). Nonzero entries in matrix G indicate the presence of an edge.

Examples

1. Create and view a directed acyclic graph (DAG) with six nodes and eight edges.

   DG = sparse([6 6 6 2 2 3 5 1],[2 5 1 3 4 5 1 4],true,6,6)
   
   DG =
   
      (5,1)        1
      (6,1)        1
      (6,2)        1
      (2,3)        1
      (1,4)        1
      (2,4)        1
      (3,5)        1
      (6,5)        1
   
   view(biograph(DG))

   

2. Find the topological order of the DAG.

   order = graphtopoorder(DG)
   
   order =
   
        6     2     3     5     1     4
   

3. Permute the nodes so that they appear ordered in the graph display.

   DG = DG(order,order)
   
   DG =
   
      (1,2)        1
      (2,3)        1
      (1,4)        1
      (3,4)        1
      (1,5)        1
      (4,5)        1
      (2,6)        1
      (5,6)        1
   
   view(biograph(DG))

   

References

[1] Siek, J.G., Lee, L-Q, and Lumsdaine, A. (2002). The Boost Graph Library User Guide and Reference Manual, (Upper Saddle River, NJ:Pearson Education).

See Also

graphallshortestpaths | graphconncomp | graphisdag | graphisomorphism | graphisspantree | graphmaxflow | graphminspantree | graphpred2path | graphshortestpath | graphtraverse | topoorder

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