Pith Number

pith:OEMB76LM

pith:2026:OEMB76LMNAWR3U3BQTFGWSNQ5H

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Directed Q-Analysis and Directed Higher-Order Connectivity on Digraphs: A Quantitative Approach

Andr\'e Fujita, Heitor Baldo, Koichi Sameshima, Luiz A. Baccal\'a

Directed graphs can be analyzed for higher-order interactions by constructing directed clique complexes that capture multi-node directed relationships.

arxiv:2605.14178 v1 · 2026-05-13 · math.GM

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Claims

C1strongest claim

we lay out a mathematical formalism resting on directed clique complexes constructed from directed graphs (their 'higher-order structures' or 'simplicial structures'), stressing the interrelations between directed cliques (their 'directed higher-order connectivities'), leading towards a more complete directed Q-analysis that allows quantifying, characterizing, and comparing similarities involving simplicial structures.

C2weakest assumption

That directed cliques can be consistently defined from digraphs and that their interrelations meaningfully capture higher-order directed interactions without additional assumptions on the underlying data.

C3one line summary

A new formalism for directed Q-analysis using directed clique complexes to quantify and compare higher-order connectivities in digraphs.

References

300 extracted · 300 resolved · 4 Pith anchors

[1] Abdelnour, F. and Dayan, M. and Devinsky, O. and Thesen, T. and Raj, A. Estimating brain's functional graph from the structural graph's Laplacian. Proceedings of SPIE

[2] Abdelnour, F. and Dayan, M. and Devinsky, O. and Thesen, T. and Raj, A. Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure. NeuroImage

[3] Achard, S. and Bullmore, E. Efficiency and Cost of Economical Brain Functional Networks. PLoS Comput Biol

[4] Aharoni, R. and Berger, E. and Meshulam, R. Eigenvalues and homology of flag complexes and vector representations of graphs. Geom. Funct. Anal

[5] Ahmadlou, M. and Adeli, H. and Adeli, A. Graph theoretical analysis of organization of functional brain networks in ADHD. Clinical EEG and neuroscience

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:11.279624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71181ff96c682d1dd36184ca6b49b0e9ddc29fee31a7127128a99cf32c0aced8

Aliases

arxiv: 2605.14178 · arxiv_version: 2605.14178v1 · doi: 10.48550/arxiv.2605.14178 · pith_short_12: OEMB76LMNAWR · pith_short_16: OEMB76LMNAWR3U3B · pith_short_8: OEMB76LM

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OEMB76LMNAWR3U3BQTFGWSNQ5H \
  | 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: 71181ff96c682d1dd36184ca6b49b0e9ddc29fee31a7127128a99cf32c0aced8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "792d1d78c4fa22c9e917b60d4ad0a83f33c3e2d3f740fa039618827905a3fc56",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-05-13T22:58:42Z",
    "title_canon_sha256": "701312d20bd3140e01327a54ce65299ac16c39945837b0bb3d214af47081b8f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14178",
    "kind": "arxiv",
    "version": 1
  }
}