{"id":"W3127781635","doi":"10.1016/j.dam.2021.01.014","title":"A relation between proximity and the third largest distance eigenvalue of a graph","year":2021,"lang":"en","type":"article","venue":"Discrete Applied Mathematics","topic":"Graph theory and applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Group for Research in Decision Analysis; HEC Montréal; University of Regina","funders":"","keywords":"Mathematics; Distance matrix; Combinatorics; Resistance distance; Distance-regular graph; Graph; Connectivity; Butterfly graph; Vertex (graph theory); Graph power; Eigenvalues and eigenvectors; Regular graph; Discrete mathematics; Line graph; Voltage 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008830101,0.0001891736,0.0004553214,0.00003809812,0.0002253642,0.00003690111,0.0002072305,0.0001012222,0.00001832178],"category_scores_gemma":[0.0002849122,0.0001306894,0.000128052,0.0003815877,0.000410329,0.0000692016,0.0001157395,0.0002085968,0.000006504047],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009958227,"about_ca_system_score_gemma":0.00003055117,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001872571,"about_ca_topic_score_gemma":0.000007745568,"domain_scores_codex":[0.9986581,0.00006800782,0.0005525119,0.0002505551,0.0002733846,0.0001973905],"domain_scores_gemma":[0.9974749,0.001304946,0.0003684087,0.0007055997,0.00008678798,0.0000593658],"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":[0.00001796479,0.00008779246,0.0002775835,0.0003748025,0.00007102171,5.666716e-7,0.002336472,0.000001680741,0.0008267848,0.9957805,0.00008787826,0.000136895],"study_design_scores_gemma":[0.0007770509,0.000007069657,0.0007129906,0.00007146651,0.0002372726,0.000005395097,0.00109598,0.0001810299,0.004681041,0.9918922,0.0001871725,0.0001513984],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6740976,0.0003267713,0.2811926,0.0008330348,0.00004255252,0.001816653,0.0001234426,0.0001632971,0.04140404],"genre_scores_gemma":[0.9416486,0.00005184929,0.05779273,0.0000338573,0.00003296451,0.0001900135,0.00002756512,0.0000300368,0.000192353],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.267551,"threshold_uncertainty_score":0.532936,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02671022364757954,"score_gpt":0.2760365620352981,"score_spread":0.2493263383877185,"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."}}