{"id":"W2950318982","doi":"10.37236/1020","title":"On Directed Triangles in Digraphs","year":2007,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Purdue University; American Institute of Mathematics; National Science Foundation","keywords":"Combinatorics; Digraph; Mathematics; Conjecture; Vertex (graph theory); Directed graph; Discrete mathematics; Graph","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001072404,0.0008840266,0.00112231,0.002337178,0.001854381,0.002326404,0.0018056,0.001487341,0.01384224],"category_scores_gemma":[0.01220776,0.0007678589,0.001151579,0.003182707,0.002167376,0.006119262,0.003751719,0.002692467,0.002245487],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001982354,"about_ca_system_score_gemma":0.0007175438,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004866198,"about_ca_topic_score_gemma":0.006539336,"domain_scores_codex":[0.9983359,0.0004687383,0.00008845338,0.0003861615,0.0004498875,0.0002709181],"domain_scores_gemma":[0.9901669,0.006592524,0.0006872726,0.001126788,0.0007488633,0.0006776651],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00009589486,0.00004391057,0.000899583,0.0001966012,0.00002016944,0.0003267377,0.0005379755,0.01416709,0.001508276,0.9506037,0.005584211,0.02601597],"study_design_scores_gemma":[0.00003519509,0.00002766647,0.0003166779,0.00005737077,0.00001689,0.0002103467,0.0001117236,0.04631187,0.0006035063,0.9397675,0.01252441,0.00001677122],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2356681,0.002937314,0.5752477,0.002815247,0.0006461009,0.000261281,0.001267902,0.0009333473,0.1802231],"genre_scores_gemma":[0.7846181,0.004402093,0.1559241,0.001771151,0.000687276,0.0005176608,0.002878048,0.0005603202,0.04864127],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01384224,"threshold_uncertainty_score":0.04630685,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01333259802547749,"score_gpt":0.2875840749563781,"score_spread":0.2742514769309006,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}