Pith Number

pith:5CJCC2BE

pith:2026:5CJCC2BE3MZRUDMJRGC2DYBLSC

not attested not anchored not stored refs resolved

Representing Higher-Order Networks: A Survey of Graph-Based Frameworks

Florentin Smarandache, Takaaki Fujita

Higher-order graph formalisms extend classical networks to model multiway, hierarchical, temporal, and multilayer interactions in complex systems.

arxiv:2605.12509 v1 · 2026-03-24 · cs.SI · cs.AI · cs.CE · math.CO

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4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Higher-order graph formalisms extend this framework by incorporating multiway, hierarchical, temporal, multilayer, recursive, and tensor-based interactions, thereby providing more expressive representations of complex systems.

C2weakest assumption

That the surveyed formalisms are representative of the field and that the structural principles and relationships are accurately described without major omissions.

C3one line summary

A comprehensive survey of graph-based formalisms for higher-order networks including multiway, hierarchical, temporal, multilayer, recursive, and tensor-based models.

References

258 extracted · 258 resolved · 1 Pith anchors

[1] Graph theory 2024

[2] Graph theory and its applications 2018

[3] Hypergraph theory 2013

[4] Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n- SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-) HyperAlgebra 2020

[5] T. Fujita. Metahypergraphs, metasuperhypergdynaraphs, and iterated metagraphs: Modeling graphs of graphs, hypergraphs of hypergraphs, superhypergraphs of superhypergraphs, and beyond. Current Research 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:10:03.079215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e892216824db331a0d898985a1e02b90a6f41d60839539ef541f3de907e49733

Aliases

arxiv: 2605.12509 · arxiv_version: 2605.12509v1 · doi: 10.48550/arxiv.2605.12509 · pith_short_12: 5CJCC2BE3MZR · pith_short_16: 5CJCC2BE3MZRUDMJ · pith_short_8: 5CJCC2BE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5CJCC2BE3MZRUDMJRGC2DYBLSC \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e892216824db331a0d898985a1e02b90a6f41d60839539ef541f3de907e49733

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aaab272003c35ecdfc8edf7fe2afae9da82fcea9c4ae466c5a458a39ce30434e",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CE",
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.SI",
    "submitted_at": "2026-03-24T03:28:40Z",
    "title_canon_sha256": "240e6ef7e85079f184acd0f30acc4933b4135f8abc01967b893379360af3508a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12509",
    "kind": "arxiv",
    "version": 1
  }
}