# Spin networks: what exactly is a trivalent node?

• I
• Heidi
In summary, Rovelli discusses spin networks and their properties, including the concept of valence for nodes in a graph. He also mentions the difference between trivalent and four valent cases and the importance of precise definitions in graph theory.
Heidi
Hi Pfs
Rovelli defines spin networks in this paper
https://arxiv.org/abs/1004.1780
for a trivalent node Vn = 0 (the volume)
nodes begin to "get" volume with the four valent case.
take a cube or a tetrahedron, each vertex is linkes to 3 nodes so they would have a null volume.
things are different if we take the reciprocal network: from a node inside a tetrahedron four edges can intersect the four faces.
then we are in the four valent case.
have we to be more precise to talk about the valence of a node?

Heidi said:
Rovelli defines spin networks in this paper

Graph theory nomenclature can be confusing, definitions must often be given to maintain the proper content.
And believe it or not some definitions are even excluded from certain theorems.
What is a valence of a node, trivalent node.
A trivalent (3-valent) graph is often called a cubic graph.
A graph consists of a set N of items called nodes (vertices, points etc.), with a set E ⊆ the set of (unordered) pairs of nodes.
The pairs that are in E are called edges (links, arcs etc.) & an edge is said to
“run between” its two nodes, its “endpoints”.

#### Attachments

• 77796.pdf
1 MB · Views: 96

• Beyond the Standard Models
Replies
2
Views
2K
• Quantum Physics
Replies
1
Views
709
• Beyond the Standard Models
Replies
1
Views
2K
• Beyond the Standard Models
Replies
1
Views
3K
• Beyond the Standard Models
Replies
14
Views
3K
• Beyond the Standard Models
Replies
2
Views
3K
• Beyond the Standard Models
Replies
13
Views
5K
• Beyond the Standard Models
Replies
20
Views
5K
• Chemistry
Replies
2
Views
830
• Beyond the Standard Models
Replies
14
Views
5K