{"id":"W2012755367","doi":"10.1016/j.laa.2005.12.020","title":"Eigenvalues of graphs and a simple proof of a theorem of Greenberg","year":2006,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Graph theory and applications","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Eigenvalues and eigenvectors; Simple (philosophy); Combinatorics; Pure mathematics","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":[0.0008064424,0.001014296,0.001094272,0.002513653,0.001292711,0.001838586,0.001451524,0.001319309,0.01062127],"category_scores_gemma":[0.003826912,0.000568954,0.00116323,0.001472347,0.002953304,0.004246335,0.002361733,0.003508811,0.001331543],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001132977,"about_ca_system_score_gemma":0.0004679871,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001181512,"about_ca_topic_score_gemma":0.0009623739,"domain_scores_codex":[0.9995456,0.0001356724,0.00002036347,0.0000724843,0.0001787197,0.00004708577],"domain_scores_gemma":[0.9986832,0.0007436963,0.00008611763,0.000129378,0.0002329657,0.0001246611],"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":[0.000009387529,0.00001495341,0.00003932311,0.00004048663,0.000008038145,0.00004501568,0.00009534047,0.0005496725,0.0007156212,0.9910676,0.003931617,0.003482924],"study_design_scores_gemma":[0.00000726901,0.000003993933,0.00006126444,0.00000775649,0.000003273932,0.00002891971,0.00001715817,0.001493261,0.0001310903,0.9954002,0.002839356,0.000006320022],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1046931,0.00810321,0.5584392,0.02628051,0.006450626,0.0001340858,0.0007218311,0.001352539,0.293825],"genre_scores_gemma":[0.8142594,0.004388238,0.1010902,0.006560864,0.004889445,0.0002861841,0.0003065878,0.0006537745,0.06756533],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01062127,"threshold_uncertainty_score":0.0355317,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01854813958535024,"score_gpt":0.2788888504103185,"score_spread":0.2603407108249683,"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."}}