Unweighted, Undirected Network (BUN) - Teradata Vantage - Background information for ML Engine LocalClusteringCoefficient function.

Machine Learning Engine Analytic Function Reference

Product
Teradata Vantage
Release Number
8.00
1.0
Published
May 2019
Language
English (United States)
Last Update
2019-11-22
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B700-4003
lifecycle
previous
Product Category
Teradata Vantage™

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