NetworkX VS SymPy

Built from this data... https://github.com/networkx/networkx/blob/main/examples/grap...

I think one of the elements that author is missing here is that graphs are sparse matrices, and thus can be expressed with Linear Algebra. They mention adjacency matrices, but not sparse adjacency matrices, or incidence matrices (which can express muti and hypergraphs).

Linear Algebra is how almost all academic graph theory is expressed, and large chunks of machine learning and AI research are expressed in this language as well. There was recent thread here about PageRank and how it's really an eigenvector problem over a matrix, and the reality is, all graphs are matrices, they're typically sparse ones.

One question you might ask is, why would I do this? Why not just write my graph algorithms as a function that traverses nodes and edges? And one of the big answers is, parallelism. How are you going to do it? Fork a thread at each edge? Use a thread pool? What if you want to do it on CUDA too? Now you have many problems. How do you know how to efficiently schedule work? By treating graph traversal as a matrix multiplication, you just say Ax = b, and let the library figure it out on the specific hardware you want to target.

Here for example is a recent question on the NetworkX repo for how to find the boundary of a triangular mesh, it's one single line of GraphBLAS if you consider the graph as a matrix:

https://github.com/networkx/networkx/discussions/7326

This brings a very powerful language to the table, Linear Algebra. A language spoken by every scientist, engineer, mathematician and researcher on the planet. By treating graphs like matrices graph algorithms become expressible as mathematical formulas. For example, neural networks are graphs of adjacent layers, and the operation used to traverse from layer to layer is matrix multiplication. This generalizes to all matrices.

There is a lot of very new and powerful research and development going on around sparse graphs with linear algebra in the GraphBLAS API standard, and it's best reference implementation, SuiteSparse:GraphBLAS:

https://github.com/DrTimothyAldenDavis/GraphBLAS

SuiteSparse provides a highly optimized, parallel and CPU/GPU supported sparse Matrix Multiplication. This is relevant because traversing graph edges IS matrix multiplication when you realize that graphs are matrices.

Recently NetworkX has grown the ability to have different "graph engine" backends, and one of the first to be developed uses the python-graphblas library that binds to SuiteSparse. I'm not a directly contributor to that particular work but as I understand it there has been great results.

In the project we used Python lib networkx and a DiGraph object (Direct Graph). To detect a table reference in a Query, we use sqlglot, a SQL parser (among other things) that works well with Bigquery.

If you program in Python, can use NetworkX for that. But it's probably a good idea to implement the basic algorithms yourself at least one time.

For those wanting to play with graphs and ML I was browsing the arangodb docs recently and I saw that it includes integrations to various graph libraries and machine learning frameworks [1]. I also saw a few jupyter notebooks dealing with machine learning from graphs [2].

Integrations include:

* NetworkX -- https://networkx.org/

* DeepGraphLibrary -- https://www.dgl.ai/

* cuGraph (Rapids.ai Graph) -- https://docs.rapids.ai/api/cugraph/stable/

* PyG (PyTorch Geometric) -- https://pytorch-geometric.readthedocs.io/en/latest/

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1: https://docs.arangodb.com/3.11/data-science/adapters/

2: https://github.com/arangodb/interactive_tutorials#machine-le...

org-roam-ui is a great interactive visualization tool, but its main use is visualization. The hope of this library is that it could be part of a larger graph analysis pipeline. The demo provides an example graph visualization, but what you choose to do with the resulting graph certainly isn't limited to that. See for example networkx.

Thank you for your interest. There are some interesting examples in the SWE-bench-lite benchmark which are resolved by AutoCodeRover:

- From sympy: https://github.com/sympy/sympy/issues/13643. AutoCodeRover's patch for it: https://github.com/nus-apr/auto-code-rover/blob/main/results...

- Another one from scikit-learn: https://github.com/scikit-learn/scikit-learn/issues/13070. AutoCodeRover's patch (https://github.com/nus-apr/auto-code-rover/blob/main/results...) modified a few lines below (compared to the developer patch) and wrote a different comment.

There are more examples in the results directory (https://github.com/nus-apr/auto-code-rover/tree/main/results).

That's interesting. You should consider yourself lucky to have met Wolfram employees, as they are obviously vastly outnumbered by users of Mathematica.

I have not met any developers for either of these products but I know that SymPy has a huge list of contributors for a project of its size. See: https://github.com/sympy/sympy/blob/master/AUTHORS

You may not be hearing about SymPy users because SymPy is not a monolithic product. It is a library. If you know mathematicians big into using Python, they are probably aware of SymPy as it is the main attraction when it comes to symbolic computation in Python.

https://github.com/sympy/sympy/issues/9479 suggests that multivariate inequalities are still unsolved in SymPy, though it looks like https://github.com/sympy/sympy/pull/21687 was merged in August. This probably isn't yet implemented in C++ in SymForce yet?

bug report opened https://github.com/sympy/sympy/issues/25507

https://news.ycombinator.com/item?id=36463580

From https://news.ycombinator.com/item?id=36159017 :

> sympy.utilities.lambdify.lambdify() https://github.com/sympy/sympy/blob/a76b02fcd3a8b7f79b3a88df... :

>> """Convert a SymPy expression into a function that allows for fast numeric evaluation [with the CPython math module, mpmath, NumPy, SciPy, CuPy, JAX, TensorFlow, SymPy, numexpr,]*

From https://westurner.github.io/hnlog/#comment-19084622 :

> "latex2sympy parses LaTeX math expressions and converts it into the equivalent SymPy form" and is now merged into SymPy master and callable with sympy.parsing.latex.parse_latex(). It requires antlr-python-runtime to be installed. https://github.com/augustt198/latex2sympy https://github.com/sympy/sympy/pull/13706

ENH: 'generate a Jupyter notebook' (nbformat .ipynb JSON) function from this stem formula

https://en.wikipedia.org/wiki/Vectorization :

> Array programming, a style of computer programming where operations are applied to whole arrays instead of individual elements

> Automatic vectorization, a compiler optimization that transforms loops to vector operations

> Image tracing, the creation of vector from raster graphics

> Word embedding, mapping words to vectors, in natural language processing

> Vectorization (mathematics), a linear transformation which converts a matrix into a column vector

Vector (disambiguation) https://en.wikipedia.org/wiki/Vector

> Vector (mathematics and physics):

> Row and column vectors, single row or column matrices

> Vector space

> Vector field, a vector for each point

And then there are a number of CS usages of the word vector for 1D arrays.

Compute kernel: https://en.m.wikipedia.org/wiki/Compute_kernel

GPGPU > Vectorization, Stream Processing > Compute kernels: https://en.wikipedia.org/wiki/General-purpose_computing_on_g...

sympy.utilities.lambdify.lambdify() https://github.com/sympy/sympy/blob/a76b02fcd3a8b7f79b3a88df... :

> """Convert a SymPy expression into a function that allows for fast numeric evaluation [with the CPython math module, mpmath, NumPy, SciPy, CuPy, JAX, TensorFlow, SymPt, numexpr,]

pyorch lambdify PR, sympytorch: https://github.com/sympy/sympy/pull/20516#issuecomment-78428...

Sympytorch:

> Turn SymPy expressions into PyTorch Modules.

> SymPy floats (optionally) become trainable parameters. SymPy symbols are inputs to the Module.

sympy2jax https://github.com/MilesCranmer/sympy2jax :

> Turn SymPy expressions into parametrized, differentiable, vectorizable, JAX functions.

> All SymPy floats become trainable input parameters. SymPy symbols become columns of a passed matrix.

Look at sympy.isprime for a carefully-optimized pure-Python solution (though if gmpy2 is installed, which it usually is, it will use that instead after trying the easiest cases)