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[2301.06712] $(k,q)$-core decomposition of hypergraphs
Source: arxiv.org
Article summary:
1. The article discusses the concept of (k,q)-core decomposition in hypergraphs and its application to identify influential subgroups.
2. It uses a random bipartite network composed of vertices and hyperedges to study the distributions of vertex degree k and hyperedge size q.
3. It reveals a hybrid percolation transition for either k≥3 or q≥3, as well as a distinguishable degree-dependent critical relaxation dynamics in the (2,2)-core decomposition process.
Article analysis:
The article is generally reliable and trustworthy, as it provides evidence for its claims through the use of generating function methods for the distributions of vertex degree k and hyperedge size q, as well as simulations to uncover a hybrid percolation transition for either k≥3 or q≥3. Furthermore, it presents both sides equally by exploring possible counterarguments to its claims. However, there are some potential biases that should be noted. For example, the article does not explore all possible risks associated with using (k,q)-core decomposition in hypergraphs, such as potential inaccuracies due to incomplete data or incorrect assumptions about the underlying structure of the hypergraphs being studied. Additionally, it does not provide any evidence for its claim that (k,q)-core decomposition can be used to select modular structures such as coauthorship groups.
Topics for further research:
Risks associated with (k,q)-core decomposition in hypergraphs
Inaccuracies due to incomplete data in (k,q)-core decomposition
Incorrect assumptions about hypergraphs in (k,q)-core decomposition
Selecting modular structures using (k,q)-core decomposition
Coauthorship groups using (k,q)-core decomposition
Generating function methods for hypergraph distributions