C

Bipartition

Show Usages
Calculates a bipartition of the given graph, if one exists.
Inheritance Hierarchy

Remarks

A graph is bipartite if its nodes can be divided into two partitions where no edges are between nodes of the same partition. Instead, every edge connects a node from the first with a node from the second partition.

Other Graph Connectivity Algorithms

yFiles for HTML supports a number of other analysis algorithms that partition the graph into components, based on various criteria.

  • ConnectedComponents – Determines components defined by the existence of an undirected path between nodes
  • StronglyConnectedComponents – Determines components defined by the existence of a directed path between nodes
  • BiconnectedComponents – Determines components defined by the existence of at least two separate undirected paths between all nodes
  • IndependentSets – Divides a graph into partitions where no nodes are connected within a partition
  • KCoreComponents – Calculates the k-cores of an undirected input graph. The k-core of an undirected input graph consists of the subgraph components where each node has at least degree k.

Complexity

O(|V| + |E|)

Examples

Calculating the two partitions of a bipartite graph
// prepare the bipartition algorithm
const algorithm = new Bipartition()
// run the algorithm
const result = algorithm.run(graph)

// highlight the nodes of the partitions with different styles
if (result.isBipartite) {
  for (const node of result.firstPartition.nodes) {
    graph.setStyle(node, firstPartitionStyle)
  }
  for (const node of result.secondPartition.nodes) {
    graph.setStyle(node, secondPartitionStyle)
  }
}

See Also

Developer's Guide

API

bipartition

Members

No filters for this type

Constructors

Bipartition

()

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 a bipartition on a subset of the graph
// configure the bipartition algorithm
const algorithm = new Bipartition({
  // 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)

// highlight the nodes of the partitions with different styles
if (result.isBipartite) {
  for (const node of result.firstPartition.nodes) {
    graph.setStyle(node, firstPartitionStyle)
  }
  for (const node of result.secondPartition.nodes) {
    graph.setStyle(node, secondPartitionStyle)
  }
}

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 bipartition on a subset of the graph
// configure the bipartition algorithm
const algorithm = new Bipartition({
  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)

// highlight the nodes of the partitions with different styles
if (result.isBipartite) {
  for (const node of result.firstPartition.nodes) {
    graph.setStyle(node, firstPartitionStyle)
  }
  for (const node of result.secondPartition.nodes) {
    graph.setStyle(node, secondPartitionStyle)
  }
}

Methods

run

(graph: IGraph): BipartitionResult
Calculates a bipartition of the given graph, if one exists.
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

BipartitionResult
A BipartitionResult containing both partitions of graph. If the graph is not bipartite, the resulting partitions are empty and isBipartite is false.

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|)