What do you think of this definition of Spin Networks?

[Heidi]

Hi Pfs
i found a paper:
https://arxiv.org/abs/math-ph/0306059
in which the author gives a definition of spin networks
it is at the bottom of page 5
the words node or vertex does not appear.
what do you think of it?
Does the author think that all the information is in the hilbert spaces on which the representations act?

 

[Heidi]

I read the paragraph too fast. the author said that what followed concerned
the case of r loops passing all through a single node (look a fig 1)

 

[Heidi]

I understand why. He only considers loops based on a single point . He constrcts then a peculiar spin network with only on node.