Expose `igraph_product()`

[szhorvat]

@gulshan-123 implemented a graph product feature in the C core as igraph_product(). It would be great to expose this in R/igraph. Two product types are already released and two more will land soon.

https://igraph.org/c/html/latest/igraph-Operators.html#igraph_product

@schochastics, what do you think a nice interface could be for this? Do we want an operator like * or %*% for the classic Cartesian product, or do we restrict this to a plain function? Other graph operators, such as union, have operators such as %u%.

For the explicit function, what's a better name? Just product() (risk of collision, but short) or graph_product()?

[schochastics]

I think product() might be fine because we also have union() . I also think an operator would be good to have but then separate ones for cartesian/tensor with "%"?
But @maelle is better at naming things than me!

[maelle]

Sounds good to me.

[szhorvat]

Perhaps this operation is just not common enough to introduce an operator form for it. If one introduced, I would only do it for the Cartesian product, which is the classic graph product concept, and which is set as the default in interfaces.yaml.

[schochastics]

Then maybe no operator. You are right, I don't think that the function is common enough that a shortcut is needed

[szhorvat]

If the graphs have vertex names, it'd be nice to auto-generate names for the product as well. For example if graph 1 has vertices A and B, and graph 2 has 3 vertices but no vertex names, the result graph could have names

A-1
A-2
A-3
B-1
B-2
B-3

Here I used - as the concatenation character. What this should be is up for debate.

[schochastics]

I have an R implementation of products here: https://github.com/schochastics/netUtils/blob/main/R/graph_products.R and I also used "-". I think it makes the most sense. The problem with autogenerating names is also touching #1932. From a consistency point, throwing an error should be correct? Or we decide on a general naming scheme for unnamed graphs. In that case I would vote for "V1..Vn". Up to debate

[szhorvat]

There's now a separate function for yet another product type that requires an extra parameter: igraph_rooted_product(). I would recommend using the same function in the R interface, with an extra argument that is valid only for this product.