Direct betweenness

[GroteGnoom]

Fixes #1796

Making cutoffs work seems like a lot of work, because the only shortest path functions with cutoffs are igraph_distances_cutoff, igraph_distances_dijkstra_cutoff, which don't actually give me the paths.

subset betweenness should be doable.
Edit:
subset betweenness is way harder than I thought.

the FINALLY stack is a mess, that still needs to be fixed.

[codecov]

Codecov Report

Merging #2352 (15c8ae8) into master (6e3d61b) will increase coverage by 0.00%.
The diff coverage is n/a.

@@           Coverage Diff           @@
##           master    #2352   +/-   ##
=======================================
  Coverage   83.46%   83.46%           
=======================================
  Files         376      376           
  Lines       61576    61576           
=======================================
+ Hits        51394    51397    +3     
+ Misses      10182    10179    -3     

Impacted Files	Coverage Δ
src/paths/all_shortest_paths.c	98.16% <ø> (+0.91%)	⬆️

... and 2 files with indirect coverage changes

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[GroteGnoom]

If I have an undirected line:

igraph_small(&graph, 5, IGRAPH_UNDIRECTED, 0,1, 1,2, -1);

and I do a subset betweenness between source 0, and target 2:

igraph_vss_range(0, 1), igraph_vss_range(2,3))

Then for vertex 1 I should get a betweenness of 1, right? Not 0.5.

The original implementation just divides the end result by 2 for undirected situations, but I think that's incorrect. That only works if your targets and sources are the same. If there's no overlap then there is no division needed at all, and if there is a little overlap, you can't use a basic division at the end to fix everything.

[szhorvat]

Making cutoffs work seems like a lot of work, because the only shortest path functions with cutoffs are igraph_distances_cutoff, igraph_distances_dijkstra_cutoff, which don't actually give me the paths.

Let's skip this until the necessary functions are implemented. #2358

[szhorvat]

If I have an undirected line:

igraph_small(&graph, 5, IGRAPH_UNDIRECTED, 0,1, 1,2, -1);

and I do a subset betweenness between source 0, and target 2:

igraph_vss_range(0, 1), igraph_vss_range(2,3))

Then for vertex 1 I should get a betweenness of 1, right? Not 0.5.

Correct.

The original implementation just divides the end result by 2 for undirected situations, but I think that's incorrect. That only works if your targets and sources are the same. If there's no overlap then there is no division needed at all, and if there is a little overlap, you can't use a basic division at the end to fix everything.

I believe you are right. I'd have to look into this in more detail to see how the subset version works and how it can be fixed most effectively.

But we are making progress, we discovered a bug, so that's good. This was precisely the purpose of the direct implementation.

[szhorvat]

Opened a new issue for this:

• igraph_betweenness_subset() gives invalid results in undirected graphs #2359

[ntamas]

I believe you are right.

Yes, you are correct. This seems to be a bug indeed. Great job!