1.0 - 8.00 - Unweighted, Undirected Network (BUN) - Teradata Vantage

Teradata® Vantage Machine Learning Engine Analytic Function Reference

Teradata Vantage
Release Number
Release Date
May 2019
Content Type
Programming Reference
Publication ID
English (United States)

The local clustering coefficient was originally defined on an unweighted, undirected graph—also called a bi-directed network (BUN). A simple BUN has no self-loops and no multiple edges.

Let G = (V, E) be a simple BUN with a set of nodes (vertices) V and a set of edges E.

The degree d i of node i is the number of nodes in V that are adjacent to i. A complete subgraph of three nodes of G is called a triangle. This is the formula for the number of triangles of node i:

where a ij = 1 if there is an edge from i to j; otherwise a ij = 0.

A triple Ƴ at a node i is a path of length two for which i is the center node. This is the formula for the maximum number of triples of node i:

The maximum number of triples occurs when every neighbor of node i is connected to every other neighbor of node i.

This is the formula for the clustering coefficient for a node i with d i ≥ 2:

c i = δ i / τ i