{"id":"W169044707","doi":"","title":"Laplacian Eigenvalues and the Excess of a Graph.","year":2002,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Graph theory and applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Eigenvalues and eigenvectors; Graph; Laplace operator; Laplacian matrix; Combinatorics; Mathematical analysis; Physics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000444395,0.0005057076,0.0005280388,0.002590594,0.00079761,0.001771527,0.0007226532,0.0008203467,0.009601569],"category_scores_gemma":[0.003516623,0.0002404463,0.0002713987,0.0009363287,0.001557708,0.002452845,0.001192903,0.0010974,0.001408302],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006567576,"about_ca_system_score_gemma":0.0002588728,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005648287,"about_ca_topic_score_gemma":0.0009088097,"domain_scores_codex":[0.9996573,0.00007984835,0.000012519,0.00005626713,0.0001297213,0.00006429684],"domain_scores_gemma":[0.9985237,0.0006565984,0.0002084198,0.000129632,0.0002005979,0.0002811386],"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":[0.00002781075,0.00001533777,0.0002960116,0.00003407217,0.000006597373,0.00009645054,0.00008675844,0.001314003,0.001551574,0.9879141,0.002757413,0.005899847],"study_design_scores_gemma":[0.000008561821,0.000009533956,0.0003894497,0.00001419737,0.000005603484,0.0001946793,0.00009218274,0.0108386,0.000382365,0.985294,0.00276162,0.000009344828],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6234607,0.004816503,0.126638,0.006761159,0.001008786,0.00003478105,0.0006576499,0.0006932673,0.2359293],"genre_scores_gemma":[0.9729279,0.001309887,0.006852129,0.0003409823,0.0005052072,0.00003290027,0.0001560432,0.00009818891,0.01777666],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009601569,"threshold_uncertainty_score":0.03212041,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03011903369141844,"score_gpt":0.2670818628958165,"score_spread":0.236962829204398,"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."}}