C

SpanningTree

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Calculates a minimum spanning tree or forest for a graph.
Inheritance Hierarchy

Remarks

Definitions

  • A spanning tree of an undirected connected graph is a subset of its edges that induce a tree that connects all nodes of the graph.
  • A minimum spanning tree of a weighted connected graph is a spanning tree whose edges have minimum overall cost among all spanning trees of that graph.

If the graph is not connected, the result is a (minimum) spanning forest instead, whose components are spanning trees.

Other Tree-Related Algorithms

yFiles for HTML supports a number of other algorithms and helpers related to trees:

  • FeedbackEdgeSet – finds edges that can be removed or reversed to make a graph into a tree
  • TreeAnalysis – analyzes directed trees and provides access to tree properties, for example, the root node, the set of leaf nodes or the depth of a node.

Complexity

  • O(|V| + |E|) for graphs with uniform-cost edges
  • O(|E| ⋅ log(|V|)) otherwise

Examples

Calculating a spanning tree of the graph
// prepare the spanning tree detection algorithm
const algorithm = new SpanningTree()
// run the algorithm
const result = algorithm.run(graph)

// Remove the edges in the reduction
for (const edge of result.edges) {
  graph.setStyle(edge, spanningTreeEdgeStyle)
}

See Also

Developer's Guide

API

minimumSpanningTree

Members

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Constructors

SpanningTree

()

Parameters

Properties

costs

: ItemMapping<IEdge, number>
Gets or sets a mapping for edge costs.
When specifying costs, the algorithm will minimize the total cost of edges that form the spanning tree.
conversionfinal

See Also

Developer's Guide

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 a spanning tree of a subset of the graph
// prepare the spanning tree detection algorithm
const algorithm = new SpanningTree({
  // 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.edges) {
  graph.setStyle(edge, spanningTreeEdgeStyle)
}

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 a spanning tree of a subset of the graph
// prepare the spanning tree detection algorithm
const algorithm = new SpanningTree({
  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.edges) {
  graph.setStyle(edge, spanningTreeEdgeStyle)
}

Methods

run

(graph: IGraph): SpanningTreeResult
Calculates a minimum spanning tree or forest for the given graph.
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

SpanningTreeResult
A SpanningTreeResult containing the edges that make up the spanning tree (or forest).

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| + |E|) for graphs with uniform-cost edges
  • O(|E| ⋅ log(|V|)) otherwise