1.1 - 8.10 - Centrality Formulas - Teradata Vantage

Teradata Vantage™ - Machine Learning Engine Analytic Function Reference

Product
Teradata Vantage
Release Number
1.1
8.10
Release Date
October 2019
Content Type
Programming Reference
Publication ID
B700-4003-079K
Language
English (United States)

Symbols Used in Centrality Formulas

Symbol Represents
G Graph
V Vertex
N Number of vertices
A Adjacency matrix of vertices
a ij Element in matrix that represents relationship between vertex i and vertex j
c i 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:


Formula for Eigenvector centrality, used by Machine Learning Engine function EigenvectorCentrality

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:


Formula for Katz centrality, used by Machine Learning Engine function EigenvectorCentrality

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:


Formula for Bonacich centrality, used by Machine Learning Engine function EigenvectorCentrality

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.