{"id":"W4410993347","doi":"10.1103/physrevresearch.7.l022050","title":"Random graphs with specific degree distribution and giant component size","year":2025,"lang":"en","type":"article","venue":"Physical Review Research","topic":"Complex Network Analysis Techniques","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"Natural Sciences and Engineering Research Council of Canada; Canada First Research Excellence Fund; Engineering Research Centers; Université Laval","keywords":"Component (thermodynamics); Degree distribution; Degree (music); Giant component; Random graph; Mathematics; Statistics; Distribution (mathematics); Combinatorics; Physics; Graph; Complex network; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0007285564,0.0001516515,0.0004809192,0.00004900916,0.0002130858,0.00007347983,0.0002262455,0.00001164579,0.0001166282],"category_scores_gemma":[0.00003121494,0.0001061083,0.0001498514,0.001017619,0.0002424857,0.00005856131,0.0001958281,0.0004033242,0.00002245828],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003941476,"about_ca_system_score_gemma":0.0000432148,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009822164,"about_ca_topic_score_gemma":0.000004170144,"domain_scores_codex":[0.9983,0.000345008,0.000213576,0.0003577768,0.0004298583,0.0003538182],"domain_scores_gemma":[0.9984172,0.0007956944,0.00004653506,0.0004166458,0.0002231529,0.0001007874],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0001816289,0.0007042607,0.004666192,0.0006925253,0.0002923823,0.000005576985,0.00002798659,0.000003244925,0.002049203,0.529754,0.05183832,0.4097847],"study_design_scores_gemma":[0.003803907,0.0004279882,0.05774477,0.01045568,0.0004826519,0.000002335572,0.00009227861,0.006061093,0.00457605,0.4093809,0.5060095,0.0009628089],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5286698,0.1648589,0.1728153,0.01585541,0.0001195133,0.0104648,0.0002805073,0.000497595,0.1064382],"genre_scores_gemma":[0.9943964,0.004694306,0.0003224981,0.0000356115,0.0001023391,0.0001912097,0.00007177875,0.000009482424,0.0001763497],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4657266,"threshold_uncertainty_score":0.4326969,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05486707360276535,"score_gpt":0.3904836278330236,"score_spread":0.3356165542302583,"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."}}