C

BiconnectedComponents

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Determines the biconnected components and articulation points of a given undirected graph.
Inheritance Hierarchy

Remarks

A biconnected component is a subgraph which is connected and non-separable, i.e. after removing one single node the component is still connected. Another way of looking at it is that every pair of nodes in a biconnected component has at least two different paths between them.

In a connected (sub)graph the biconnected components are attached to each other at shared nodes, the so-called articulation points. Articulation points represent nodes that, when removed, cause the whole connected component to break up into multiple connected components.

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
  • Bipartition – Divides a graph into two partitions where all edges have their source and target in different partitions
  • 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

Highlighting the edges of different biconnected components in a graph
// prepare the biconnected components algorithm
const algorithm = new BiconnectedComponents()
// run the algorithm
const result = algorithm.run(graph)

// highlight the edges of the biconnected components with different styles
for (const edge of graph.edges) {
  const componentId = result.edgeComponentIds.get(edge)!
  graph.setStyle(edge, componentStyles.get(componentId)!)
}

See Also

Developer's Guide

API

biconnectedComponents

Members

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Constructors

BiconnectedComponents

()

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 biconnected components on a subset of the graph
// configure the biconnected components algorithm
const algorithm = new BiconnectedComponents({
  // 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 edges of the biconnected components with different styles
for (const edge of graph.edges) {
  const componentId = result.edgeComponentIds.get(edge)!
  graph.setStyle(edge, componentStyles.get(componentId)!)
}

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 biconnected components on a subset of the graph
// configure the biconnected components algorithm
const algorithm = new BiconnectedComponents({
  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 edges of the biconnected components with different styles
for (const edge of graph.edges) {
  const componentId = result.edgeComponentIds.get(edge)!
  graph.setStyle(edge, componentStyles.get(componentId)!)
}

Methods

run

(graph: IGraph): BiconnectedComponentsResult
Determines the biconnected components and articulation points of a given undirected 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

BiconnectedComponentsResult
A BiconnectedComponentsResult containing the biconnected components and articulation points 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| + |E|)