C

TransitiveReduction

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Calculates the transitive reduction for a directed acyclic graph.
Inheritance Hierarchy

Remarks

Given G = (V, E) be a directed acyclic graph. The transitive reduction of G is a graph which contains an edge (v, w) only if no path exists from v to w in G of length 2 or more.

Other Transitivity Algorithms

yFiles for HTML supports other algorithms related to transitivity:

  • TransitiveClosure – calculates the transitive closure of a graph, i.e. the edges that would have to be added that the set of edges defines the reachability relation in the graph
  • TransitiveEdges – calculates the edges which connect the visible nodes in a graph if these are indirectly connected via hidden nodes.

Complexity

O(|V|³)

Examples

Calculating the transitive reduction of a graph
// prepare the transitive reduction algorithm
const algorithm = new TransitiveReduction()
// run the algorithm
const result = algorithm.run(graph)

// Remove the edges in the reduction
for (const edge of result.edgesToRemove) {
  graph.remove(edge)
}

See Also

Developer's Guide

API

applyTransitiveReduction

Members

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Constructors

TransitiveReduction

()

Parameters

Properties

subgraphEdges

: ItemCollection<IEdge>
Gets or sets the collection of edges which define a subset of the graph for the algorithms to work on.

If nothing is set, all edges of the graph will be processed.

If only the excludes are set all edges in the graph except those provided in the excludes are processed.

Note that edges which start or end at nodes which are not in the subgraphNodes are automatically not considered by the algorithm.

ItemCollection<T> instances may be shared among algorithm instances and will be (re-)evaluated upon (re-)execution of the algorithm.

The edges provided here must be part of the graph which is passed to the run method.
conversionfinal

Examples

Calculating the transitive reduction of a subset of the graph
// prepare the transitive reduction algorithm
const algorithm = new TransitiveReduction({
  // Ignore edges without target arrow heads
  subgraphEdges: {
    excludes: (edge: IEdge): boolean =>
      edge.style instanceof PolylineEdgeStyle &&
      edge.style.targetArrow instanceof Arrow &&
      edge.style.targetArrow.type === ArrowType.NONE,
  },
})
// run the algorithm
const result = algorithm.run(graph)

// Remove the edges in the reduction
for (const edge of result.edgesToRemove) {
  graph.remove(edge)
}

subgraphNodes

: ItemCollection<INode>
Gets or sets the collection of nodes which define a subset of the graph for the algorithms to work on.

If nothing is set, all nodes of the graph will be processed.

If only the excludes are set, all nodes in the graph except those provided in the excludes are processed.

ItemCollection<T> instances may be shared among algorithm instances and will be (re-)evaluated upon (re-)execution of the algorithm.

The nodes provided here must be part of the graph which is passed to the run method.
conversionfinal

Examples

Calculating the transitive reduction of a subset of the graph
// prepare the transitive reduction algorithm
const algorithm = new TransitiveReduction({
  subgraphNodes: {
    // only consider elliptical nodes in the graph
    includes: (node: INode): boolean =>
      node.style instanceof ShapeNodeStyle &&
      node.style.shape === ShapeNodeShape.ELLIPSE,
    // but ignore the first node, regardless of its shape
    excludes: graph.nodes.first()!,
  },
})
// run the algorithm
const result = algorithm.run(graph)

// Remove the edges in the reduction
for (const edge of result.edgesToRemove) {
  graph.remove(edge)
}

Methods

run

(graph: IGraph): TransitiveReductionResult
Calculates the transitive reduction for a directed acyclic graph.
This implementation is costly in terms of memory, since a (n × n) matrix is allocated to store reach data.
The result obtained from this algorithm is a snapshot which is no longer valid once the graph has changed, e.g. by adding or removing nodes or edges.
final

Parameters

graph: IGraph
The input graph to run the algorithm on.

Return Value

TransitiveReductionResult
A TransitiveReductionResult containing the transitive edges of the given graph. Removing those edges results in the transitive reduction of graph.

Throws

Exception ({ name: 'InvalidOperationError' })
If the algorithm can't create a valid result due to an invalid graph structure or wrongly configured properties.

Complexity

O(|V|³)