{"paper":{"title":"Directed Q-Analysis and Directed Higher-Order Connectivity on Digraphs: A Quantitative Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Directed graphs can be analyzed for higher-order interactions by constructing directed clique complexes that capture multi-node directed relationships.","cross_cats":[],"primary_cat":"math.GM","authors_text":"Andr\\'e Fujita, Heitor Baldo, Koichi Sameshima, Luiz A. Baccal\\'a","submitted_at":"2026-05-13T22:58:42Z","abstract_excerpt":"Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes interact simultaneously. This has led many to develop network topology analysis methods based on higher-order structures and higher-order connectivity, seeking to reveal complex interactions beyond node pairs. Many of the latter address only undirected networks. To overcome this, we lay out a mathematical formalism resting on directed clique complexes constructed"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new formalism for directed Q-analysis using directed clique complexes to quantify and compare higher-order connectivities in digraphs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Directed graphs can be analyzed for higher-order interactions by constructing directed clique complexes that capture multi-node directed relationships.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9bfbceaf7dcd1713b30bc8df735d307b8cb294a7d4c045b3e1dc0e0830d515d2"},"source":{"id":"2605.14178","kind":"arxiv","version":1},"verdict":{"id":"c1840247-71a4-4a2c-9d56-3598ab5278b4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:49:03.246253Z","strongest_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.","one_line_summary":"A new formalism for directed Q-analysis using directed clique complexes to quantify and compare higher-order connectivities in digraphs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"Directed graphs can be analyzed for higher-order interactions by constructing directed clique complexes that capture multi-node directed relationships."},"references":{"count":300,"sample":[{"doi":"","year":null,"title":"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","work_id":"e91ac279-d6fe-4955-9b77-c2739217fff5","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"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","work_id":"dedd6bc2-2d9c-4537-aad2-c85825dcf249","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Achard, S. and Bullmore, E. Efficiency and Cost of Economical Brain Functional Networks. PLoS Comput Biol","work_id":"f082db03-3131-46eb-9076-f3152f6b68f1","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Aharoni, R. and Berger, E. and Meshulam, R. Eigenvalues and homology of flag complexes and vector representations of graphs. Geom. Funct. Anal","work_id":"c6c19a62-f5de-45f2-8c32-f6634348b125","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Ahmadlou, M. and Adeli, H. and Adeli, A. Graph theoretical analysis of organization of functional brain networks in ADHD. Clinical EEG and neuroscience","work_id":"7c961119-58f2-482a-8486-5ab48083644c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":300,"snapshot_sha256":"566e27380f668a2aab4ce1750d33afe5e807877c9deb39dee64701be83080b00","internal_anchors":4},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8724ca9cfb4d4d602efeefe4a1ab8f14823bf9347ba3db9b044a37362042e167"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}