Update Betweenness Centrality normalization #4974
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ChuckHastings
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python/cugraph/cugraph/tests/centrality/test_betweenness_centrality.py
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…ality.py Co-authored-by: Erik Welch <[email protected]>
| } | ||
| } else if (graph_view.number_of_vertices() > 2) { | ||
| scale_factor = static_cast<weight_t>( | ||
| std::min(static_cast<vertex_t>(num_sources), graph_view.number_of_vertices() - 1) * |
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No need to subtract 1 from num_sources? (i.e. static_cast<vertex_t>(num_sources - 1)?)
I assume num_sources == graph_view.number_of_vertices() for full BC. It looks a bit weird to subtract 1 just from graph_view.number_of_vertices().
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We had some complex gyrations around the formulas.
There are a couple of things being accounted for in the scaling factor. In the normalization path, we're trying to divide by the maximum number of times a vertex could appear in the shortest paths. For the full graph, since we're not including endpoints, this is (n-1) * (n-2) where n is the number of vertices in the graph. This would occur for a vertex v that has an input edge from every vertex in the graph. The n-1 factor counts every vertex other than v (when we start at v we won't travel back to v and we're not counting the endpoint). and the n-2 factor is the maximum number of paths that could travel through v.
For approximate betweenness, we're only traveling through num_sources samples. So the maximum value would be num_sources * n-2. This would occur in any combination of the above described graph where the randomly selected sources did not include the vertex v.
I agree it looks odd.
| scale_factor = (graph_view.is_symmetric() ? weight_t{2} : weight_t{1}) * | ||
| static_cast<weight_t>(num_sources) / | ||
| (include_endpoints ? static_cast<weight_t>(graph_view.number_of_vertices()) | ||
| : static_cast<weight_t>(graph_view.number_of_vertices() - 1)); |
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We don't check vertices.size() (or sum of vertices.size() in multi-GPU) > 0. So, it is technically possible to pass empty seed vertices, and in this case, num_sources = 0 && graph_view.number_of_verties() = 1 is possible; then, scale_factor can become 0 leading to divide by 0.
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Good catch. That check exists in the above if statements and not this one. I will add that.
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Just pushed an update
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/merge |
Betweenness Centrality normalization is not quite right if you specify not including endpoints and use approximate betweenness.
This PR temporarily disables some of the python tests that compare results with networkx, since the networkx to update the normalization scores is not yet merged. Once networkx/networkx#7908 is merged we should be able to create another PR to enable those tests. Each of the disabled tests is skipped with a link to that PR as the reason.
Closes #4941