## Class ClosenessCentrality<V,​E>

• Type Parameters:
V - the graph vertex type
E - the graph edge type
All Implemented Interfaces:
VertexScoringAlgorithm<V,​Double>
Direct Known Subclasses:
HarmonicCentrality

public class ClosenessCentrality<V,​E>
extends Object
implements VertexScoringAlgorithm<V,​Double>
Closeness centrality.

Computes the closeness centrality of each vertex of a graph. The closeness of a vertex $x$ is defined as the reciprocal of the farness, that is $H(x)= 1 / \sum_{y \neq x} d(x,y)$, where $d(x,y)$ is the shortest path distance from $x$ to $y$. When normalization is used, the score is multiplied by $n-1$ where $n$ is the total number of vertices in the graph. For more details see wikipedia and

• Alex Bavelas. Communication patterns in task-oriented groups. J. Acoust. Soc. Am, 22(6):725–730, 1950.

This implementation computes by default the closeness centrality using outgoing paths and normalizes the scores. This behavior can be adjusted by the constructor arguments.

When the graph is disconnected, the closeness centrality score equals $0$ for all vertices. In the case of weakly connected digraphs, the closeness centrality of several vertices might be 0. See HarmonicCentrality for a different approach in case of disconnected graphs.

Shortest paths are computed either by using Dijkstra's algorithm or Floyd-Warshall depending on whether the graph has edges with negative edge weights. Thus, the running time is either $O(n (m +n \log n))$ or $O(n^3)$ respectively, where $n$ is the number of vertices and $m$ the number of edges of the graph.

Author:
Dimitrios Michail
• ### Field Detail

• #### graph

protected final Graph<V,​E> graph
Underlying graph
• #### incoming

protected final boolean incoming
Whether to use incoming or outgoing paths
• #### normalize

protected final boolean normalize
Whether to normalize scores
• #### scores

protected Map<V,​Double> scores
The actual scores
• ### Constructor Detail

• #### ClosenessCentrality

public ClosenessCentrality​(Graph<V,​E> graph)
Construct a new instance. By default the centrality is normalized and computed using outgoing paths.
Parameters:
graph - the input graph
• #### ClosenessCentrality

public ClosenessCentrality​(Graph<V,​E> graph,
boolean incoming,
boolean normalize)
Construct a new instance.
Parameters:
graph - the input graph
incoming - if true incoming paths are used, otherwise outgoing paths
normalize - whether to normalize by multiplying the closeness by $n-1$, where $n$ is the number of vertices of the graph
• ### Method Detail

• #### getShortestPathAlgorithm

protected ShortestPathAlgorithm<V,​E> getShortestPathAlgorithm()
Get the shortest path algorithm for the paths computation.
Returns:
the shortest path algorithm
• #### compute

protected void compute()
Compute the centrality index