Add triangles #3
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I think the tests could be improved. Some of the NetworkX tests get coverage, but only compare to 0 triangles. Also, we should test more with self-edges. There may be better ways to compute triangles for: - all nodes - a subset of nodes - a single node There are *a lot* of different ways to compute triangles, so this could be explored further in the future. I hope the current PR is competitive.
graphblas_algorithms/cluster.py Outdated
| def single_triangle_core(G, index): | ||
| M = Matrix(bool, G.nrows, G.ncols) | ||
| M[index, index] = False | ||
| C = any_pair(G.T @ M.T).new(name="C") # select.coleq(G, index) |
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Check it out, @jim22k, a use case for coleq select op!
Hmm, the comment is wrong. Should be select.coleq(G.T, index) or select.col(G.T == index).
Triangle counting raises the inevitable question: how should we handle properties (such as For now, they are passed as arguments to functions and computed if necessary. |
| C = plus_pair(L @ L.T).new(mask=L.S) | ||
| return ( | ||
| C.reduce_rowwise().new(mask=mask) | ||
| + C.reduce_columnwise().new(mask=mask) | ||
| + plus_pair(U @ L.T).new(mask=U.S).reduce_rowwise().new(mask=mask) | ||
| ).new(name="triangles") |
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I wish I had an intuitive explanation for why this worked (I'm sure one exists if you twist your brain just so). There are simpler methods, but this implementation seems pretty fast.
Here's an example of a simpler method:
L = gb.select.tril(G, -1).new(name="L")
B = gb.select.offdiag(G).new(name="offdiag")
return plus_pair(B @ L.T).new(mask=B.S).reduce_rowwise().new(mask=mask)
I think the tests could be improved. Some of the NetworkX tests get coverage,
but only compare to 0 triangles. Also, we should test more with self-edges.
There may be better ways to compute triangles for:
There are a lot of different ways to compute triangles, so this could be
explored further in the future. I hope the current PR is competitive.