Remarks
Closeness centrality is defined as the reciprocal of the sum of shortest path distances of a node to all other nodes in the graph. Therefore, a node with high closeness centrality has short distances to all other nodes of a graph.
Other Centrality Measures
yFiles for HTML supports a number of other centrality measures:
- GraphCentrality – emphasizes nodes that have short paths to other nodes in a slightly different way
- DegreeCentrality – emphasizes nodes with many edges
- WeightCentrality – emphasizes nodes with highly-weighted edges
- BetweennessCentrality – emphasizes nodes that are part of many short paths
- EigenvectorCentrality – computes the influence a node has on a network. The centrality value is higher if more nodes are connected to that node
- PageRank – computes page rank values for all nodes based on their attached edges
Complexity
- O(|V|² + |V| ⋅ |E|) for unweighted graphs
- O(|V| ⋅ |E| + |V|² ⋅ log |V|) for weighted graphs
Examples
const result = new ClosenessCentrality({
directed: true,
// Use the geometric edge length as weight
weights: (edge) =>
edge.style.renderer
.getPathGeometry(edge, edge.style)
.getPath()!
.getLength(),
}).run(graph)
// add node labels for centrality values
// and adjust node size according to centrality
result.normalizedNodeCentrality.forEach(({ key, value }) => {
const node = key
const centrality = value
graph.addLabel(key, String(value))
graph.setNodeLayout(
node,
new Rect(node.layout.center, new Size(centrality, centrality)),
)
})See Also
Developer's Guide
API
- closenessCentrality
Members
Constructors
Properties
true.Property Value
true if the graph should be considered as directed, false otherwise.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 that 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.
Examples
const result = new ClosenessCentrality({
directed: true,
// Use the geometric edge length as weight
weights: (edge) =>
edge.style.renderer
.getPathGeometry(edge, edge.style)
.getPath()!
.getLength(),
// 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(graph)
// add node labels for centrality values
// and adjust node size according to centrality
result.normalizedNodeCentrality.forEach((entry) => {
const node = entry.key
const centrality = entry.value
graph.addLabel(node, `${centrality}`)
graph.setNodeLayout(
node,
new Rect(node.layout.center, new Size(centrality, centrality)),
)
})Gets or sets the collection of nodes which define a subset of the graph for the algorithms to work on.
If nothing is set, all nodes of the graph will be processed.
If only the excludes are set, all nodes in the graph except those provided in the excludes are processed.
ItemCollection<T> instances may be shared among algorithm instances and will be (re-)evaluated upon (re-)execution of the algorithm.
Examples
const result = new ClosenessCentrality({
directed: true,
// Use the geometric edge length as weight
weights: (edge) =>
edge.style.renderer
.getPathGeometry(edge, edge.style)
.getPath()!
.getLength(),
subgraphNodes: {
// only consider elliptical nodes in the graph
includes: (node: INode): boolean =>
node.style instanceof ShapeNodeStyle &&
node.style.shape === ShapeNodeShape.ELLIPSE,
// but ignore the first node, regardless of its shape
excludes: graph.nodes.first()!,
},
}).run(graph)
// add node labels for centrality values
// and adjust node size according to centrality
result.normalizedNodeCentrality.forEach((entry) => {
const node = entry.key
const centrality = entry.value
graph.addLabel(node, `${centrality}`)
graph.setNodeLayout(
node,
new Rect(node.layout.center, new Size(centrality, centrality)),
)
})Gets or sets a mapping for edge weights.
Closeness centrality computes shortest paths throughout the graph. Edge weights influence the computed length of those paths and thus the centrality measure. If no weights are provided, all edges have the same uniform weight of 1 and the number of edges is effectively the shortest path length.
Edge weights for closeness centrality must be positive.
Methods
Computes the closeness centrality for the nodes of a graph.
Parameters
- graph: IGraph
- The input graph to run the algorithm on.
Return Value
- ClosenessCentralityResult
- A ClosenessCentralityResult from which the calculated centrality values can be obtained.
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|² + |V| ⋅ |E|) for unweighted graphs
- O(|V| ⋅ |E| + |V|² ⋅ log |V|) for weighted graphs