Understanding LQG: Adding and Multiplying in Spin Networks

[naima]

Hi all

I use to read posts on LQG where I try to understand what will be evident next 10 years!.
I'd just like to know how one can add to spin networks or multiply one by a scalar?

Thank you

 

[naima]

in fact my question is about union or concatenation: given two graphs is there a natural operation producing a connex graph with the sum of volumes.
the same fom 1 graph to get a new graph with a volume multiplied by a scalar

 

[cesiumfrog]

I also have a "layman's" question:

What has been achieved so far in LQG,
and where are the best resources teaching how to do those kinds of calculation with LQG (and also what sort of background is prerequisite for such)?