Definition:Metagraph

Definition
A metagraph $\mathcal G$ consists of:
 * objects $X, Y, Z, \ldots$
 * morphisms $f, g, h, \ldots$ between its objects

A metagraph is purely axiomatic, and does not use set theory.

For example, the objects are not "elements of the set of objects", because these axioms are (without further interpretation) unfounded in set theory.

Terminology
The objects of a metagraph are also called vertices or nodes.

The morphisms of a metagraph are also called edges or arrows.

The domain of a morphism is also called its origin or source.

The codomain of a morphism is also called its destination or target

Also see

 * Graph