methods to work with hypergraphs structures

Repository for collection of computer science methods and mathematical approaches to work with hypergraph structures. Some of the details and motivation to develop this techniques is explained here https://sites.google.com/view/liubovkmatematike/research-projects/graphs-and-hypergraphs

methods comparison

We are working and comparing various existing frameworks and computational languages

1. Here we explore the computational languages of python (numpy and non-numpy frameworks) to calculate the graph rewriting systems https://github.com/Liyubov/hypergraphs_structures/blob/main/code%20notebooks/hyper_graph_motif_counting_rewriting_numpy.ipynb
2. Here we expore other existing packages for computing projected hypergraph properties https://github.com/Liyubov/hypergraphs_structures

methods and existing repositories

There are specific thematic resources dedicated to the analysis of the hypergraph structures:

1. hypercore decomposition analysis https://github.com/marco-mancastroppa/hypercore-decomposition
2. hypergraph motifs analysis https://github.com/FraLotito/higher-order-motifs
3. hypergraph rewriting (recent work in progress on testing Mathematica integrated module) https://github.com/Liyubov/hypergraphs_structures/ related to this large part of work is developed and inspired by Wolfram Institute work https://github.com/phcerdan/wolfram_model

The tutorials repository is https://github.com/xgi-org/xgi/tree/main/tutorials

analytical approaches

The existing approaches towards studying hypergraph structures and n-arity itself is described in the recent works from Carlos Zapatta and collaborators working on ("Beyond Binary: Hypermatrix Algebra and Irreducible Arity in Higher-Order Systems")[https://www.researchgate.net/publication/367251087_Beyond_Binary_Hypermatrix_Algebra_and_Irreducible_Arity_in_Higher-Order_Systems] with the aim to connect both algebraic and geometric structures.

testing examples of the hypergraphs

Here we test the basic example of the knowledge hypergraph, generated from the arxiv data and motivated on the recent work presented in https://arxiv.org/abs/2107.03749 and https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0270131

This is in the joint effort and collaboration with Carlos Zapata, who have shared the open problems and priniciples in the hypergraph theory, author of the framework https://arity.science/