1
$\begingroup$

Let $\mathcal{G} = (\mathcal{N}, \mathcal{L})$ represent a directed graph, where $\mathcal{N}$ is the set of nodes.

What would be the correct way to represent the set of links between them?

$$\mathcal{L} = \{(i,j) \mid i,j \in \mathcal{S}, i \neq j \}\rightarrow$$ Is this correct?

Does this imply that $\mathcal{L}$ contains all such $(i,j)$ pairs? Because it would be wrong to assume that the graph is a complete graph.

$\endgroup$
0
$\begingroup$

You can represent the set of links as $ \mathcal{L} \subset \mathcal{N} \times \mathcal{N} $. The crossproduct is all the pairs and subset indicates that not all pairs are present. Also typically directional graphs don’t prohibit nodes that have an edge to themselves.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.