Find Eigenvector Centrality Scores of Network Positions
evcent takes a graph (
graph) and returns the
eigenvector centralities of positions
v within it
- Graph to be analyzed.
- Numeric vector indicating which vertices are to be included in the calculation. By default, all vertices are included.
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 high-density substructures). This is also intelligible from an algebraic point of view, with the first eigenvector being closely related to the best rank-1 approximation of the adjacency matrix (a relationship which is easy to see in the special case of a diagonalizable symmetric real matrix via the $SLS^-1$ decomposition).)
- A vector containing the centrality scores.
evcent will not symmetrize your data before
extracting eigenvectors; don't send this routine asymmetric matrices
unless you really mean to do so.
Bonacich, P. (1987). Power and Centrality: A Family of Measures. American Journal of Sociology, 92, 1170-1182.
Katz, L. (1953). A New Status Index Derived from Sociometric Analysis. Psychometrika, 18, 39-43.
#Generate some test data g <- graph.ring(10, directed=FALSE) #Compute eigenvector centrality scores evcent(g)