Originally Posted by

**dunsta** Sorry, i tried to simplify a larger question, and obviously am showing my weakness in this subject.

The 'set' I mention is actually a set of vertices on a graph.

So imagine

v1 = (1,1) i.e. a loop

v2 = (2,2) another loop

v3 = (3,3) another loop

V1 connects to v2 (1,2)

v2 connects to v3 (2,3)

the relationship is defined by (v,w) E R: if there is atleast one edge in graph which connects vertex V to W directly.

then I have a second graph that is same as graph 1, but has the edge (1,3) i.e. connecting v1 to v3, making an equivalence relation, (I believe).

What is the induced partition on the set V?