7.00.02 - Unweighted, Undirected Network (BUN) - Aster Analytics

Teradata Aster® Analytics Foundation User GuideUpdate 2

Product
Aster Analytics
Release Number
7.00.02
Release Date
September 2017
Content Type
Programming Reference
User Guide
Publication ID
B700-1022-700K
Language
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. The number of triangles of node i is:



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. The maximum number of triples of node i is:



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

The clustering coefficient for a node i with d i ≥ 2 is:

c i = δ i / τ i