Symbols Used in Centrality Formulas
| Symbol | Represents |
|---|---|
| G | Graph |
| V | Vertex |
| N | Number of vertices |
| A | Adjacency matrix of vertices |
| aij | Element in matrix that represents relationship between vertex i and vertex j |
| ci | Centrality value of vertex i |
Eigenvector Centrality
Bonacich (1972) suggests that the eigenvector of the largest eigenvalue of an adjacency matrix could make a good network centrality measure. He defines Eigenvector Centrality as:
For more information about this formula, see:
Bonacich, P. Factoring and Weighting Approaches to Status Scores and Clique Identification. Journal of Mathematical Sociology 2 (1972), 113-120.
Katz Centrality
Katz (1953) gives a measure of centrality as:
For more information about this formula, see:
Katz, L. A New Status Index Derived from Sociometric Analysis. Psychometrika 18 (1953), 39-43.
Bonacich Centrality
Bonacich (1987) writes a more generic centrality measure as:
a and b are exchanged in the above formula (compared to the original one) to be consistent with Katz centrality.
For more information about this formula, see:
Bonacich, P. Power and Centrality: A Family of Measures. American Journal of Sociology 92 (1987), 1170-1182.