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

Teradata Aster® Analytics Foundation User GuideUpdate 2

Aster Analytics
Release Number
Release Date
September 2017
Content Type
Programming Reference
User Guide
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. 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