Chapter 9: Fundamental Physics

Section 7: Space as a Network

Generalizations [of trivalent networks]

Almost any kind of generalized network can be emulated by a trivalent network just by introducing more nodes. As indicated in the main text, networks with more than three connections at each node can be emulated by combining nodes into groups, and looking only at the connections between groups. Networks with colored nodes can be emulated by representing each color of node by a fixed group of nodes. Going beyond ordinary networks, one can consider hypernetworks in which connections join not just pairs of nodes, but larger numbers of nodes. Such hypernetworks are specified by adjacency tensors rather than adjacency matrices. But it is possible to emulate any hypernetwork by having each generalized connection correspond to a group of connections in an ordinary trivalent network.

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