Penrose's definition A spin network, as described in Penrose (1971),R. Penrose (1971a), "Angular momentum: an approach to combinatorial spacetime," in T. Bastin (ed.), Quantum Theory and Beyond, Cambridge University Press (this paper can be found online on John C. Baez's website); and R. Penrose (1971b), "Applications of negative dimensional tensors," in D. J. A. Welsh (ed.), Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969), Academic Press, pp. 221–244, esp. p. 241 (the latter paper was presented in 1969 but published in 1971 according to Roger Penrose, "On the Origins of Twistor Theory" (Archived June 23, 2021) in: Gravitation and Geometry, a Volume in Honour of I. Robinson, Biblipolis, Naples 1987). is a kind of diagram in which each line segment represents the world line of a "unit" (either an elementary particle or a compound system of particles). Three line segments join at each vertex. A vertex may be interpreted as an event in which either a single unit splits into two or two units collide and join into a single unit. Diagrams whose line segments are all joined at vertices are called closed spin networks. Time may be viewed as going in one direction, such as from the bottom to the top of the diagram, but for closed spin networks the direction of time is irrelevant to calculations.
Penrose's definition A spin network as described in Penrose (1971)R Penrose (1971a) "Angular momentum an approach to combinatorial spacetime" in T Bastin (ed) Quantum Theory and Beyond Cambridge University Press (this paper can be found online on John C Baez's website); and R Penrose (1971b) "Applications of negative dimensional tensors" in D J A Welsh (ed) Combinatorial Mathematics and its Applications (Proc Conf Oxford 1969) Academic Press pp 221–244 esp p 241 (the latter paper was presented in 1969 but published in 1971 according to Roger Penrose "On the Origins of Twistor Theory" (Archived June 23 2021) in Gravitation and Geometry a Volume in Honour of I Robinson Biblipolis Naples 1987) is a kind of diagram in which each line segment represents the world line of a "unit" (either an elementary particle or a compound system of particles) Three line segments join at each vertex A vertex may be interpreted as an event in which either a single unit splits into two or two units collide and join into a single unit Diagrams whose line segments are all joined at vertices are called closed spin networks Time may be viewed as going in one direction such as from the bottom to the top of the diagram but for closed spin networks the direction of time is irrelevant to calculations