`issymmetric(::SimpleDiGraph)` not correct

[jlapeyre]

This dispatches here

Graphs.jl/src/operators.jl

Line 498 in 53cb581

issymmetric(g::AbstractGraph) = !is_directed(g)

This of course returns false for any digraph, and digraphs can indeed be symmetric.

I don't know how many meanings of symmetric are common in fields using graphs. But wikipedia says this means that for each edge $(v, w)$ there is an edge $(w, v)$.

[simonschoelly]

I agree with you here. I think if we change it, we have to do it, so that it is still true for all undirected graphs. For directed graphs I am not sure if there is an easy way to that so have some default for all directed AbstractGraph or if we simply should return a not-implemented message.

[etiennedeg]

Should it also take into account weights or metadata ?

[gdalle]

Should it also take into account weights or metadata ?

Weight maybe, metadata we can't do it anyway in the current state of affairs

[gdalle]

But Graphs.jl itself doesn't have a method for getting the weight of an edge. Best we could do is to add an optional argument weights passing a matrix? But who would ever use this function anyway?

[simonschoelly]

Should it also take into account weights or metadata ?

I think the solution that we currently have in #248 kind of solves this, although certainly there are other ways to handle that. It basically uses the edges(g), reverse(e), has_edge(g, e), and e1 == e2 functions to verify if a graph is symmetric. If some graph type has some weights/edge-metadata and correctly implements these functions, then symmetry is correctly checked.

Of course one could argue, that there should be a way to ignore weights/metadata but I am not sure how important that is. perhaps in the future, we can specify that with an additional parameter.