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There is an API formalizing this style of matrix/graph computation called GraphBLAS, coming soon to a language and database near you.

Here is an easy to read but math focused introduction to the topic by Dr Jeremy Kepner Head and Founder of the MIT Lincoln Laboratory Supercomputing Center:

http://www.mit.edu/~kepner/GraphBLAS/GraphBLAS-Math-release....

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What do you mean "coming soon" -- GraphBLAS 2.3.0 was just released [1] -- it's been here! ;)

[1] http://faculty.cse.tamu.edu/davis/GraphBLAS.html

[2] http://graphblas.org

For more context, depth, and previous discussions, see...

https://hn.algolia.com/?query=GraphBLAS&sort=byPopularity&pr...

It's true. I look forward to seeing more language bindings, like Python, Javascript, etc. I expect it will be soon. For my own GraphBLAS education I have been working on a PostgreSQL extension:

https://github.com/michelp/pggraphblas

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