TOPICS

# Multiway Graph

A multiway graph is a graph representing all possible branches of evolution for a system. Each node in the graph represents a possible complete state of the system at a particular step, while each edge corresponds to the evolution of one state to another as a result of an updating event. In a causally invariant system, every branching in the multiway system must ultimately reconverge (Wolfram).

For example, the illustration above shows the multiway graph for the evaluation of the Fibonacci number using its standard recursive definition. The path followed by the Wolfram Language's standard evaluator is delineated in red (Wolfram 2023).

Multicomputation, Multiway System

## References

Wolfram, S. "Appendix: Graph Types: Multiway States Graph (Multiway Graph)." https://www.wolframphysics.org/technical-introduction/additional-material/appendix-graph-types/.Wolfram, S. "Expression Evaluation and Fundamental Physics: Multiway Evaluation and Multiway Graphs." Sep. 29, 2023. https://writings.stephenwolfram.com/2023/09/expression-evaluation-and-fundamental-physics/#multiway-evaluation-and-multiway-graphs.

## Cite this as:

Weisstein, Eric W. "Multiway Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MultiwayGraph.html