degree of loops about graphs.jl

[simonschoelly]

I feel like I have seen this question before, but maybe it was about something else.

I am not sure if this is a bug, or a deliberate choice to just return the length of the adjacency list - as this is computationally very efficient. It also matches what the documentation states, namely

for undirected graphs, it equals the connected edges.

But as probably every textbook defines this differently we should probably change this eventually.

I would propose, that we would add the following functions

num_neighbors(g, v)  # return the number of connected neighbors (inclusive itself in case of a self-loop

num_edges(g, v)  # number of connected edges

Maybe of the difficult to wrote num_neighbors we could also write num_vertices(g, v) - not sure about that though. num_edges might also be helpful, if we ever implement multigraphs.

Of course we also would then create the directed versions of these functions for directed graphs. Btw, I am not sure, how much degree makes sense for directed graphs - it is the indegree plus the outdegree, so

julia> gd = SimpleDiGraph([Edge(1, 1)]);
julia> degree(gd, 1)
2

so in this case this seems correct.

I am not completely sure how we should proceed about degree - maybe it would make sense to deprecate the degree functions for a while altogether, and then later reintroduce them with a changed behavior?