gives a list of eigenvector centralities for the vertices in the graph g.
gives a list of in-centralities for a directed graph g.
gives a list of out-centralities for a directed graph g.
uses rules vw to specify the graph g.
Details and Options
- EigenvectorCentrality will give high centralities to vertices that are connected to many other well-connected vertices.
- EigenvectorCentrality gives a list of centralities that can be expressed as a weighted sum of centralities of its neighbors.
- With being the largest eigenvalue of the adjacency matrix for the graph g, you have:
EigenvectorCentrality[g] EigenvectorCentrality[g,"In"] , left eigenvector EigenvectorCentrality[g,"Out"] , right eigenvector
- Eigenvector centralities are normalized.
- For a directed graph g, EigenvectorCentrality[g] is equivalent to EigenvectorCentrality[g,"In"].
- The option WorkingPrecision->p can be used to control precision used in internal computations.
- EigenvectorCentrality works with undirected graphs, directed graphs, multigraphs, and mixed graphs.
Examplesopen allclose all
Basic Examples (2)
By default, EigenvectorCentrality finds centralities using machine-precision computations:
Highlight the eigenvector centrality for CycleGraph:
Properties & Relations (6)
Use and as the parameters for KatzCentrality:
Use VertexIndex to obtain the centrality of a specific vertex:
Wolfram Research (2010), EigenvectorCentrality, Wolfram Language function, https://reference.wolfram.com/language/ref/EigenvectorCentrality.html (updated 2015).
Wolfram Language. 2010. "EigenvectorCentrality." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/EigenvectorCentrality.html.
Wolfram Language. (2010). EigenvectorCentrality. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EigenvectorCentrality.html