Chapter 9: Fundamental Physics

Section 8: The Relationship of Space and Time

Symmetric graphs

The constraints in a network constraint system require that the structure around each node agrees with a template that contains some number of nodes. A symmetric graph satisfies the same type of constraint, but with the template being the whole network. The pictures below show the smallest few symmetric graphs with 3 connections at each node (with up to 100 nodes there are still only 37 such graphs; compare page 1029).

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]