{"id":"W2017826398","doi":"10.1016/j.laa.2011.03.051","title":"On the extremal values of the second largest Q-eigenvalue","year":2011,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Graph theory and applications","field":"Mathematics","cited_by":26,"is_retracted":false,"has_abstract":false,"ca_institutions":"Group for Research in Decision Analysis; HEC Montréal","funders":"","keywords":"Mathematics; Eigenvalues and eigenvectors; Combinatorics; Graph; Simple (philosophy); Algebraic connectivity; Laplace operator; Laplacian matrix; Simple graph; Connectivity; Discrete mathematics; Mathematical analysis","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002571568,0.0001058391,0.000110506,0.00002571314,0.0003629254,0.000008864077,0.0003284802,0.00005548756,0.0005808361],"category_scores_gemma":[0.00007619429,0.00005882116,0.00007656863,0.0002313659,0.000142306,0.00003462801,0.000068087,0.0001413442,0.00005461404],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000003430875,"about_ca_system_score_gemma":0.00001617095,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002063973,"about_ca_topic_score_gemma":0.000007626039,"domain_scores_codex":[0.9993262,0.00006288903,0.0002139869,0.0001688629,0.0001065199,0.0001215483],"domain_scores_gemma":[0.99872,0.0004783977,0.0001242876,0.0005753295,0.000061117,0.00004087628],"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":[0.000003461952,0.0001357293,0.00008008164,0.00001982156,0.00001908225,2.962927e-8,0.0005136869,1.705849e-7,0.001407333,0.996906,0.0007521274,0.0001625117],"study_design_scores_gemma":[0.00008933229,0.00001894869,0.00159866,0.00001258565,0.00003978852,0.000002885007,0.0001870873,0.000103731,0.03149437,0.9598182,0.006553695,0.00008073942],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.972388,0.0001379594,0.00151229,0.0007557913,0.0000287407,0.0009997274,0.0001008504,0.00005261719,0.02402399],"genre_scores_gemma":[0.9959824,0.00001662688,0.000850197,0.0002573931,0.0000514004,0.0003274464,0.000002812023,0.00001636038,0.002495359],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03708778,"threshold_uncertainty_score":0.6359749,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05802043641645613,"score_gpt":0.2738958967890918,"score_spread":0.2158754603726357,"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."}}