{"id":"W2951319419","doi":"10.48550/arxiv.math/0610089","title":"Geodesics and almost geodesic cycles in random regular graphs","year":2006,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Geodesic; Combinatorics; Mathematics; Distance; Wheel graph; Path graph; Graph; Random graph; Vertex (graph theory); Limiting; Shortest path problem; Discrete mathematics; Graph power; Geometry; Line 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":[0.001987045,0.0007237983,0.001047459,0.003695823,0.001760473,0.002150826,0.001608808,0.00166559,0.003481207],"category_scores_gemma":[0.01652134,0.000811039,0.001051613,0.002036538,0.003889906,0.004734861,0.002556267,0.001593191,0.0004307617],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002589405,"about_ca_system_score_gemma":0.0006660218,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001946,"about_ca_topic_score_gemma":0.001457581,"domain_scores_codex":[0.9987009,0.0005376492,0.0000614579,0.0002696579,0.0002684051,0.0001620203],"domain_scores_gemma":[0.9914953,0.00475321,0.001353038,0.0007184613,0.0006694198,0.001010636],"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":[0.00006223687,0.00002403618,0.001619713,0.00008800223,0.00002677857,0.000142557,0.0003592274,0.01679667,0.0009359899,0.9723067,0.001363731,0.006274405],"study_design_scores_gemma":[0.00002019828,0.00002537083,0.0007436724,0.00002811371,0.000008470255,0.000175419,0.00007948283,0.06028892,0.0003172208,0.9362796,0.002015341,0.00001815112],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7266896,0.004401395,0.2401963,0.002929261,0.0001035907,0.000157222,0.0006891541,0.0003726419,0.02446078],"genre_scores_gemma":[0.9628334,0.001840511,0.0282958,0.0002860098,0.000172341,0.000267926,0.000546137,0.0001244006,0.0056334],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003695823,"threshold_uncertainty_score":0.01878756,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04438902033501865,"score_gpt":0.2881495062161992,"score_spread":0.2437604858811805,"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."}}