Added strong_product, disjunctive_product, lexicographical_product, h…

[dstahlke]

Added most of the graph products from https://en.wikipedia.org/wiki/Graph_product

[codecov]

Codecov Report

Merging #154 (b7fab71) into master (897e183) will increase coverage by 0.03%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #154      +/-   ##
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+ Coverage   97.40%   97.43%   +0.03%     
==========================================
  Files         109      109              
  Lines        6470     6560      +90     
==========================================
+ Hits         6302     6392      +90     
  Misses        168      168              

[aurorarossi]

Hi! We recently added a JuliaFormatter and this pull request was made earlier, so it was not aligned. I fixed this problem and now the controls are fine except for one, since the homomorphic product is not tested. It would be great if you could provide one.
Thank you!

[simonschoelly]

Does this operator also work for directed graphs? And does it really make sense to define it for all graph types? Maybe we should restrict it to SimpleGraph and maybe also SimpleDiGraph.

Otherwise it might be a bit confusing if one has, for example, a graph with metadata on its vertices.

[dstahlke]

Though I don't see mention in wikipedia of directed graphs in relation to any of these products, I think most of them would make sense. The only exception would be the homomorphic product which has (h_1 \nsim h_2) in its definition and there could be controversy over how that should be interpreted for directed graphs. Also this one is pretty obscure and I suspect nobody would ever want to use it on a directed graph.

Good point on not supporting graphs that have metadata. What would be the appropriate way to support both SimpleGraph and SimpleDiGraph? Should I use the common parent class AbstractSimpleGraph? (Note that the existing functions tensor_product and cartesian_product also have this issue.)

[gdalle]

Making a round of unresolved PR conversations

Metadata is not supported anywhere in Graphs.jl, that is why I don't think it's a requirement for graph products.

The real issue is that these products require adding edges, and we can't guarantee this is supported beyond Simplegraphs. Furthermore, there is the question of types: what should a product of two GridGraphs be for instance? Fall back on a SimpleGraph type?

[dstahlke]

Is there anything needed from me? Should I make it take only SimpleGraph arguments rather than AbstractGraph? And if so, should I make the already existing graph product functions do the same?

[gdalle]

I think restricting these new functions to AbstractSimpleGraph would make sense for now, but without touching the existing ones (cause that might be breaking)

[dstahlke]

I changed SimpleGraph to AbstractSimpleGraph and fixed the doctests. The doctests had some trivial problems due to lines copied from tensor_product and somehow must not have been running before.