eigen_centrality  R Documentation 
eigen_centrality
takes a graph (graph
) and returns the
eigenvector centralities of positions v
within it
eigen_centrality( graph, directed = FALSE, scale = TRUE, weights = NULL, options = arpack_defaults )
graph 
Graph to be analyzed. 
directed 
Logical scalar, whether to consider direction of the edges in directed graphs. It is ignored for undirected graphs. 
scale 
Logical scalar, whether to scale the result to have a maximum score of one. If no scaling is used then the result vector has unit length in the Euclidean norm. 
weights 
A numerical vector or 
options 
A named list, to override some ARPACK options. See

Eigenvector centrality scores correspond to the values of the first eigenvector of the graph adjacency matrix; these scores may, in turn, be interpreted as arising from a reciprocal process in which the centrality of each actor is proportional to the sum of the centralities of those actors to whom he or she is connected. In general, vertices with high eigenvector centralities are those which are connected to many other vertices which are, in turn, connected to many others (and so on). (The perceptive may realize that this implies that the largest values will be obtained by individuals in large cliques (or highdensity substructures). This is also intelligible from an algebraic point of view, with the first eigenvector being closely related to the best rank1 approximation of the adjacency matrix (a relationship which is easy to see in the special case of a diagonalizable symmetric real matrix via the $S Λ S^{1}$ decomposition).)
The adjacency matrix used in the eigenvector centrality calculation assumes that loop edges are counted twice; this is because each loop edge has two endpoints that are both connected to the same vertex, and you could traverse the loop edge via either endpoint.
In the directed case, the left eigenvector of the adjacency matrix is calculated. In other words, the centrality of a vertex is proportional to the sum of centralities of vertices pointing to it.
Eigenvector centrality is meaningful only for connected graphs. Graphs that are not connected should be decomposed into connected components, and the eigenvector centrality calculated for each separately. This function does not verify that the graph is connected. If it is not, in the undirected case the scores of all but one component will be zeros.
Also note that the adjacency matrix of a directed acyclic graph or the adjacency matrix of an empty graph does not possess positive eigenvalues, therefore the eigenvector centrality is not defined for these graphs. igraph will return an eigenvalue of zero in such cases. The eigenvector centralities will all be equal for an empty graph and will all be zeros for a directed acyclic graph. Such pathological cases can be detected by checking whether the eigenvalue is very close to zero.
From igraph version 0.5 this function uses ARPACK for the underlying
computation, see arpack
for more about ARPACK in igraph.
A named list with components:
vector 
A vector containing the centrality scores. 
value 
The eigenvalue corresponding to the calculated eigenvector, i.e. the centrality scores. 
options 
A named
list, information about the underlying ARPACK computation. See

Gabor Csardi csardi.gabor@gmail.com and Carter T. Butts (http://www.faculty.uci.edu/profile.cfm?faculty_id=5057) for the manual page.
Bonacich, P. (1987). Power and Centrality: A Family of Measures. American Journal of Sociology, 92, 11701182.
#Generate some test data g < make_ring(10, directed=FALSE) #Compute eigenvector centrality scores eigen_centrality(g)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.