{ "graph": { "total_trips": 142199201, "self_loop_trips": 6460370, "self_loop_share_pct": 4.543, "n_nodes_total": 260, "n_nodes_active": 262, "n_edges_full": 42347, "edge_weight_threshold": 500, "n_nodes_filtered": 228, "n_edges_filtered": 7945, "blog_tract_nodes": 580, "blog_top_edges": 1275, "n_zones_geocoded": 260, "n_nodes_table": 263 }, "metrics": { "degree_summary": { "full_in_degree_max": 249, "full_out_degree_max": 260, "full_mean_in_degree": 161.0, "filtered_edges": 7945, "filtered_nodes": 228 }, "hub_asymmetry": { "penn_station": { "zone": "Penn Station/Madison Sq West", "in_strength": 3897451, "in_degree": 224, "trips_per_source": 17399.3 }, "midtown_center": { "zone": "Midtown Center", "in_strength": 5159038, "in_degree": 225, "trips_per_source": 22929.1 }, "times_sq": { "zone": "Times Sq/Theatre District", "in_strength": 4348768, "in_degree": 233, "trips_per_source": 18664.2 }, "jfk": { "zone": "JFK Airport", "in_strength": 1123029, "in_degree": 249, "trips_per_source": 4510.2 }, "laguardia": { "zone": "LaGuardia Airport", "in_strength": 1727487, "in_degree": 237, "trips_per_source": 7289.0 }, "east_village": { "zone": "East Village", "in_strength": 3535216, "in_degree": 219, "trips_per_source": 16142.5 }, "lower_east_side": { "zone": "Lower East Side", "in_strength": 1593653, "in_degree": 206, "trips_per_source": 7736.2 } }, "baseline_community": { "method": "python-louvain (single seed, undirected projection)", "seed": 42, "n_communities": 4, "modularity_Q": 0.1897, "n_nodes": 228, "n_edges": 5255 }, "manhattan_ends_examples": [ { "zone": "Alphabet City", "trips_per_source": 4104.5, "periphery_pct": 0.81 }, { "zone": "Lower East Side", "trips_per_source": 7736.2, "periphery_pct": 0.854 }, { "zone": "East Village", "trips_per_source": 16142.5, "periphery_pct": 0.964 } ], "manhattan_ends_most_peripheral": [ { "zone": "Marine Park/Floyd Bennett Field", "trips_per_source": 10.2 }, { "zone": "Mariners Harbor", "trips_per_source": 10.6 }, { "zone": "Pelham Bay Park", "trips_per_source": 11.2 }, { "zone": "Breezy Point/Fort Tilden/Riis Beach", "trips_per_source": 13.1 }, { "zone": "Great Kills", "trips_per_source": 15.9 }, { "zone": "Saint Michaels Cemetery/Woodside", "trips_per_source": 16.2 }, { "zone": "Grymes Hill/Clifton", "trips_per_source": 16.9 }, { "zone": "New Dorp/Midland Beach", "trips_per_source": 18.1 } ] }, "temporal": { "monthly": { "by_month": { "Jan": 12374747, "Feb": 12076079, "Mar": 12960677, "Apr": 12718147, "May": 12820628, "Jun": 12016559, "Jul": 11276541, "Aug": 10851281, "Sep": 10941959, "Oct": 11999324, "Nov": 11006595, "Dec": 11156664 }, "peak_month": "Mar", "spring_mean": 12833150, "jun_dec_mean": 11321274, "spring_to_rest_drop_pct": 11.8 }, "hour_weekday": { "weekday_morning_6_9_share_pct": 12.62, "weekend_latenight_0_4_share_pct": 5.91, "busiest_cell": { "weekday": 4, "hour": 19 } }, "cost_duration": { "sample_size": 300000, "jfk_flatfare_share_pct": 2.029, "jfk_fare_median": 52.0, "jfk_fare_iqr": [ 52.0, 52.0 ], "constant_band_49_53_share_pct": 2.187, "constant_band_is_jfk_pct": 92.7 } }, "analysis": { "centrality_rank_correlation": { "columns": [ "out_strength", "in_strength", "pagerank", "hits_hub", "hits_authority", "betweenness", "eigenvector" ], "spearman": [ [ 1.0, 0.966, 0.889, 0.989, 0.959, 0.354, 0.961 ], [ 0.966, 1.0, 0.923, 0.951, 0.998, 0.374, 0.997 ], [ 0.889, 0.923, 1.0, 0.854, 0.921, 0.516, 0.925 ], [ 0.989, 0.951, 0.854, 1.0, 0.946, 0.337, 0.946 ], [ 0.959, 0.998, 0.921, 0.946, 1.0, 0.379, 0.999 ], [ 0.354, 0.374, 0.516, 0.337, 0.379, 1.0, 0.382 ], [ 0.961, 0.997, 0.925, 0.946, 0.999, 0.382, 1.0 ] ] }, "structure": { "weighted_reciprocity": 0.818, "garlaschelli_loffredo_rho": 0.515, "mean_flow_imbalance": 0.603, "median_flow_imbalance": 0.678, "degree_assortativity": -0.184, "max_kcore": 147 }, "rich_club": { "richness_percentiles": [ 50, 70, 80, 90, 95 ], "rho_weighted_normalised": [ 2.175, 4.218, 6.735, 10.023, 10.284 ], "null": "strength-preserving weight reshuffle" }, "distance_decay": { "beta_euclidean": 0.72, "beta_se": 0.0049, "beta_trip_distance": 0.846, "pseudo_r2_deviance": 0.939, "n_edges_modelled": 41997, "note": "O,D are taxi-activity marginals so this RECONSTRUCTS more than it explains; the residual field below uses the non-circular doubly-constrained model." }, "gravity_residual_field": { "beta_doubly_constrained": 1.146, "cpc_doubly_constrained": 0.816, "obs_mean_trip_distance_mi": 2.25, "most_underconnected_core_zones": [ { "zone": "Upper East Side North", "surprise": -20.28 }, { "zone": "Upper West Side South", "surprise": -16.32 }, { "zone": "Upper East Side South", "surprise": -16.13 }, { "zone": "Upper West Side North", "surprise": -15.68 }, { "zone": "Lincoln Square East", "surprise": -12.3 }, { "zone": "Manhattan Valley", "surprise": -11.35 }, { "zone": "Yorkville East", "surprise": -9.94 }, { "zone": "Lincoln Square West", "surprise": -8.24 } ], "most_overconnected_core_zones": [ { "zone": "Times Sq/Theatre District", "surprise": 9.4 }, { "zone": "Midtown South", "surprise": 6.26 }, { "zone": "Clinton East", "surprise": 5.23 }, { "zone": "Garment District", "surprise": 4.63 }, { "zone": "Midtown East", "surprise": 4.1 }, { "zone": "Midtown Center", "surprise": 3.78 }, { "zone": "Penn Station/Madison Sq West", "surprise": 2.36 }, { "zone": "Seaport", "surprise": 1.06 } ], "east_village_les_in_core": [ { "zone": "East Village", "surprise": -5.09, "core_percentile": 0.291 }, { "zone": "Alphabet City", "surprise": -4.3, "core_percentile": 0.345 }, { "zone": "Two Bridges/Seward Park", "surprise": -1.82, "core_percentile": 0.6 }, { "zone": "Chinatown", "surprise": -0.1, "core_percentile": 0.764 }, { "zone": "Lower East Side", "surprise": 0.77, "core_percentile": 0.836 } ] }, "backbone": { "alpha": 0.05, "backbone_edges": 6190, "backbone_nodes": 262, "backbone_trip_share_pct": 87.6, "threshold_edges": 7945, "threshold_trip_share_pct": 98.6, "full_edges": 42347 }, "communities": { "algorithms": { "igraph_multilevel": { "n_communities": 4, "modularity": 0.1862 }, "leiden_modularity": { "n_communities": 4, "modularity": 0.1893 }, "infomap_directed": { "n_communities": 1, "modularity": 0.0 }, "nx_greedy_modularity": { "n_communities": 3 }, "nx_label_propagation": { "n_communities": 1 } }, "resolution_sweep": { "0.5": 17, "0.75": 7, "1.0": 4, "1.25": 5, "1.5": 10, "2.0": 16 }, "seed_stability": { "n_runs": 100, "community_count_mode": 4, "community_count_range": [ 3, 4 ], "mean_ARI": 0.751, "min_ARI": 0.421, "mean_AMI": 0.737, "n_pairs": 4950 }, "vs_administrative": { "leiden_vs_borough_AMI": 0.387, "leiden_vs_borough_ARI": 0.25, "leiden_vs_servicezone_AMI": 0.237 }, "within_community_trip_share": 0.498, "modularity_significance": { "null": "weight-concentration: edge weights reshuffled, topology and Leiden partition fixed (tests that the partition groups high-flow edges)", "Q_observed": 0.1893, "Q_null_mean": -0.0216, "z_score": 13.8 } }, "temporal_networks": { "am_peak_top_hubs": [ "Midtown Center", "Midtown East", "Times Sq/Theatre District", "Union Sq", "Midtown North", "Murray Hill", "Upper East Side South", "Upper East Side North" ], "late_night_top_hubs": [ "East Village", "Clinton East", "Murray Hill", "East Chelsea", "Gramercy", "Lower East Side", "Penn Station/Madison Sq West", "West Village" ], "am_vs_night_hub_jaccard": 0.2, "am_pm_netflow_flip": { "Midtown Center": { "nfi_am": -0.567, "nfi_pm": 0.128 }, "Financial District North": { "nfi_am": -0.205, "nfi_pm": 0.241 }, "Penn Station/Madison Sq West": { "nfi_am": 0.26, "nfi_pm": 0.03 }, "East Village": { "nfi_am": 0.492, "nfi_pm": -0.168 }, "Lower East Side": { "nfi_am": 0.372, "nfi_pm": -0.209 }, "Upper East Side North": { "nfi_am": 0.17, "nfi_pm": -0.001 }, "Times Sq/Theatre District": { "nfi_am": -0.358, "nfi_pm": 0.014 } }, "nightlife_rank_shift": { "East Village": { "am_rank": 42, "night_rank": 1 }, "Lower East Side": { "am_rank": 51, "night_rank": 6 }, "Greenwich Village North": { "am_rank": 29, "night_rank": 29 }, "Meatpacking/West Village West": { "am_rank": 41, "night_rank": 19 }, "Clinton East": { "am_rank": 22, "night_rank": 2 } }, "rhythm_clusters": { "0": { "size": 24, "peak_hour": 8, "examples": [ "Upper East Side South", "Upper East Side North", "Murray Hill", "Penn Station/Madison Sq West", "Upper West Side South" ] }, "1": { "size": 7, "peak_hour": 23, "examples": [ "Lower East Side", "Williamsburg (North Side)", "Williamsburg (South Side)", "Park Slope", "Fort Greene" ] }, "2": { "size": 11, "peak_hour": 7, "examples": [ "Astoria", "Sunnyside", "Central Harlem North", "Brooklyn Heights", "Hamilton Heights" ] }, "3": { "size": 37, "peak_hour": 21, "examples": [ "Midtown Center", "Midtown East", "Union Sq", "Times Sq/Theatre District", "Clinton East" ] } } } }, "evolution": { "panel": [ { "year": 2015, "n_nodes": 262, "n_edges": 42347, "density": 0.6193, "total_trips": 135738831, "self_trips": 6460370, "mean_trip_distance_mi": 3.071, "gravity_beta": 1.146, 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North", "in_strength": 3973497 }, { "zone_id": 170, "zone": "Murray Hill", "in_strength": 3936812 } ] }, { "year": 2017, "n_nodes": 263, "n_edges": 39752, "density": 0.5769, "total_trips": 105019197, "self_trips": 5397914, "mean_trip_distance_mi": 3.031, "gravity_beta": 1.207, "gravity_cpc": 0.807, "degree_assortativity": -0.167, "reciprocity_rho": 0.479, "weighted_reciprocity": 0.808, "modularity_Q": 0.2079, "n_communities": 4, "max_kcore": 138, "global_efficiency": 0.1676, "schneider_R_random": 0.5019, "top_hubs": [ { "zone_id": 161, "zone": "Midtown Center", "in_strength": 3963522 }, { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 3605635 }, { "zone_id": 170, "zone": "Murray Hill", "in_strength": 3424909 } ] }, { "year": 2018, "n_nodes": 261, "n_edges": 47182, "density": 0.6953, "total_trips": 94844805, "self_trips": 5043242, "mean_trip_distance_mi": 3.047, "gravity_beta": 1.207, "gravity_cpc": 0.806, "degree_assortativity": -0.163, "reciprocity_rho": 0.569, "weighted_reciprocity": 0.807, "modularity_Q": 0.2116, "n_communities": 4, "max_kcore": 165, "global_efficiency": 0.17, "schneider_R_random": 0.5014, "top_hubs": [ { "zone_id": 161, "zone": "Midtown Center", "in_strength": 3677820 }, { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 3445056 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 3221387 } ] }, { "year": 2019, "n_nodes": 262, "n_edges": 50424, "density": 0.7374, "total_trips": 78199119, "self_trips": 4229753, "mean_trip_distance_mi": 3.133, "gravity_beta": 1.223, "gravity_cpc": 0.803, "degree_assortativity": -0.131, "reciprocity_rho": 0.593, "weighted_reciprocity": 0.802, "modularity_Q": 0.2145, "n_communities": 4, "max_kcore": 181, "global_efficiency": 0.1685, "schneider_R_random": 0.4996, "top_hubs": [ { "zone_id": 161, "zone": "Midtown Center", "in_strength": 3060917 }, { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 2961071 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 2804218 } ] }, { "year": 2020, "n_nodes": 261, "n_edges": 47661, "density": 0.7023, "total_trips": 22772137, "self_trips": 1222448, "mean_trip_distance_mi": 2.979, "gravity_beta": 1.28, "gravity_cpc": 0.796, "degree_assortativity": -0.128, "reciprocity_rho": 0.594, "weighted_reciprocity": 0.796, "modularity_Q": 0.228, "n_communities": 4, "max_kcore": 171, "global_efficiency": 0.1687, "schneider_R_random": 0.4976, "top_hubs": [ { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 976160 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 882297 }, { "zone_id": 161, "zone": "Midtown Center", "in_strength": 797677 } ] }, { "year": 2021, "n_nodes": 261, "n_edges": 48451, "density": 0.714, "total_trips": 28739686, "self_trips": 1206132, "mean_trip_distance_mi": 3.247, "gravity_beta": 1.124, "gravity_cpc": 0.804, "degree_assortativity": -0.128, "reciprocity_rho": 0.61, "weighted_reciprocity": 0.791, "modularity_Q": 0.1985, "n_communities": 3, "max_kcore": 173, "global_efficiency": 0.169, "schneider_R_random": 0.4975, "top_hubs": [ { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 1274332 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 1193477 }, { "zone_id": 161, "zone": "Midtown Center", "in_strength": 955118 } ] }, { "year": 2022, "n_nodes": 261, "n_edges": 42594, "density": 0.6277, "total_trips": 36838916, "self_trips": 1375869, "mean_trip_distance_mi": 3.555, "gravity_beta": 1.029, "gravity_cpc": 0.811, "degree_assortativity": -0.171, "reciprocity_rho": 0.551, "weighted_reciprocity": 0.78, "modularity_Q": 0.1758, "n_communities": 4, "max_kcore": 153, "global_efficiency": 0.1683, "schneider_R_random": 0.4974, "top_hubs": [ { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 1513617 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 1423004 }, { "zone_id": 161, "zone": "Midtown Center", "in_strength": 1367740 } ] }, { "year": 2023, "n_nodes": 261, "n_edges": 43986, "density": 0.6482, "total_trips": 35521878, "self_trips": 1414091, "mean_trip_distance_mi": 3.526, "gravity_beta": 1.085, "gravity_cpc": 0.807, "degree_assortativity": -0.162, "reciprocity_rho": 0.585, "weighted_reciprocity": 0.764, "modularity_Q": 0.1954, "n_communities": 3, "max_kcore": 161, "global_efficiency": 0.1687, "schneider_R_random": 0.4985, "top_hubs": [ { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 1492371 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 1412529 }, { "zone_id": 161, "zone": "Midtown Center", "in_strength": 1392372 } ] }, { "year": 2024, "n_nodes": 261, "n_edges": 49178, "density": 0.7247, "total_trips": 38041717, "self_trips": 1557978, "mean_trip_distance_mi": 3.437, "gravity_beta": 1.116, "gravity_cpc": 0.803, "degree_assortativity": -0.123, "reciprocity_rho": 0.648, "weighted_reciprocity": 0.783, "modularity_Q": 0.2064, "n_communities": 3, "max_kcore": 183, "global_efficiency": 0.1692, "schneider_R_random": 0.4982, "top_hubs": [ { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 1581109 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 1504638 }, { "zone_id": 161, "zone": "Midtown Center", "in_strength": 1429662 } ] } ], "community_alignment": [ { "year_from": 2015, "year_to": 2016, "n_shared_zones": 262, "ari": 0.5355, "ami": 0.566 }, { "year_from": 2016, "year_to": 2017, "n_shared_zones": 263, "ari": 0.946, "ami": 0.8818 }, { "year_from": 2017, "year_to": 2018, "n_shared_zones": 261, "ari": 0.8658, "ami": 0.8475 }, { "year_from": 2018, "year_to": 2019, "n_shared_zones": 261, "ari": 0.9119, "ami": 0.8825 }, { "year_from": 2019, "year_to": 2020, "n_shared_zones": 261, "ari": 0.9433, "ami": 0.8433 }, { "year_from": 2020, "year_to": 2021, "n_shared_zones": 260, "ari": 0.9362, "ami": 0.8491 }, { "year_from": 2021, "year_to": 2022, "n_shared_zones": 261, "ari": 0.9165, "ami": 0.7988 }, { "year_from": 2022, "year_to": 2023, "n_shared_zones": 261, "ari": 0.9045, "ami": 0.7962 }, { "year_from": 2023, "year_to": 2024, "n_shared_zones": 261, "ari": 0.9855, "ami": 0.9702 } ], "story": { "years_processed": [ 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024 ], "n_years": 10, "volume_change_2015_2019_pct": -42.4, "covid_collapse_2019_2020_pct": -70.9, "recovery_2020_to_2024_pct": 67.1, "volume_vs_2019_at_2024_pct": 48.6, "structural_metric_variation": { "density": { "mean": 0.6647, "cv": 0.0856, "min": 0.5769, "max": 0.7374 }, "degree_assortativity": { "mean": -0.1529, "cv": 0.1488, "min": -0.184, "max": -0.123 }, "reciprocity_rho": { "mean": 0.5648, "cv": 0.0929, "min": 0.479, "max": 0.648 }, "weighted_reciprocity": { "mean": 0.796, "cv": 0.0209, "min": 0.764, "max": 0.818 }, "modularity_Q": { "mean": 0.2021, "cv": 0.0744, "min": 0.1758, "max": 0.228 }, "n_communities": { "mean": 3.6, "cv": 0.1434, "min": 3.0, "max": 4.0 }, "max_kcore": { "mean": 161.5, "cv": 0.098, "min": 138.0, "max": 183.0 }, "gravity_beta": { "mean": 1.1593, "cv": 0.0638, "min": 1.029, "max": 1.28 }, "gravity_cpc": { "mean": 0.8064, "cv": 0.0068, "min": 0.796, "max": 0.816 }, "global_efficiency": { "mean": 0.1687, "cv": 0.0038, "min": 0.1676, "max": 0.17 } }, "total_trips_cv": 0.6075 }, "notes": "Per-year diagnostics on the directed/weighted/spatial taxi-flow graph (self-loops excluded). beta/CPC are the doubly-constrained Furness gravity (same definition as analysis.gravity_residual_field). Leiden on the undirected weighted projection. Schneider R is random-failure only (giant SCC, seed-averaged, coarse-stepped) - random failure is near-flat on this dense graph; targeted-attack robustness lives in the single-year robustness module." }, "by_year": { "2015": { "evolution": { "year": 2015, "n_nodes": 262, "n_edges": 42347, "density": 0.6193, "total_trips": 135738831, "self_trips": 6460370, "mean_trip_distance_mi": 3.071, "gravity_beta": 1.146, "gravity_cpc": 0.816, "degree_assortativity": -0.184, "reciprocity_rho": 0.515, "weighted_reciprocity": 0.818, "modularity_Q": 0.1845, "n_communities": 3, "max_kcore": 147, "global_efficiency": 0.169, "schneider_R_random": 0.5015, "top_hubs": [ { "zone_id": 161, "zone": "Midtown Center", "in_strength": 5159038 }, { "zone_id": 170, "zone": "Murray Hill", "in_strength": 4394731 }, { "zone_id": 230, "zone": "Times Sq/Theatre District", "in_strength": 4348768 } ] } }, "2016": { "evolution": { "year": 2016, "n_nodes": 263, "n_edges": 41421, "density": 0.6011, "total_trips": 121820930, "self_trips": 5950421, "mean_trip_distance_mi": 3.075, "gravity_beta": 1.176, "gravity_cpc": 0.811, "degree_assortativity": -0.172, "reciprocity_rho": 0.504, "weighted_reciprocity": 0.811, "modularity_Q": 0.1988, "n_communities": 4, "max_kcore": 143, "global_efficiency": 0.1682, "schneider_R_random": 0.5031, "top_hubs": [ { "zone_id": 161, "zone": "Midtown Center", "in_strength": 4596464 }, { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 3973497 }, { "zone_id": 170, "zone": "Murray Hill", "in_strength": 3936812 } ] } }, "2017": { "evolution": { "year": 2017, "n_nodes": 263, "n_edges": 39752, "density": 0.5769, "total_trips": 105019197, "self_trips": 5397914, "mean_trip_distance_mi": 3.031, "gravity_beta": 1.207, "gravity_cpc": 0.807, "degree_assortativity": -0.167, "reciprocity_rho": 0.479, "weighted_reciprocity": 0.808, "modularity_Q": 0.2079, "n_communities": 4, "max_kcore": 138, "global_efficiency": 0.1676, "schneider_R_random": 0.5019, "top_hubs": [ { "zone_id": 161, "zone": "Midtown Center", "in_strength": 3963522 }, { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 3605635 }, { "zone_id": 170, "zone": "Murray Hill", "in_strength": 3424909 } ] } }, "2018": { "evolution": { "year": 2018, "n_nodes": 261, "n_edges": 47182, "density": 0.6953, "total_trips": 94844805, "self_trips": 5043242, "mean_trip_distance_mi": 3.047, "gravity_beta": 1.207, "gravity_cpc": 0.806, "degree_assortativity": -0.163, "reciprocity_rho": 0.569, "weighted_reciprocity": 0.807, "modularity_Q": 0.2116, "n_communities": 4, "max_kcore": 165, "global_efficiency": 0.17, "schneider_R_random": 0.5014, "top_hubs": [ { "zone_id": 161, "zone": "Midtown Center", "in_strength": 3677820 }, { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 3445056 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 3221387 } ] } }, "2019": { "evolution": { "year": 2019, "n_nodes": 262, "n_edges": 50424, "density": 0.7374, "total_trips": 78199119, "self_trips": 4229753, "mean_trip_distance_mi": 3.133, "gravity_beta": 1.223, "gravity_cpc": 0.803, "degree_assortativity": -0.131, "reciprocity_rho": 0.593, "weighted_reciprocity": 0.802, "modularity_Q": 0.2145, "n_communities": 4, "max_kcore": 181, "global_efficiency": 0.1685, "schneider_R_random": 0.4996, "top_hubs": [ { "zone_id": 161, "zone": "Midtown Center", "in_strength": 3060917 }, { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 2961071 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 2804218 } ] } }, "2020": { "evolution": { "year": 2020, "n_nodes": 261, "n_edges": 47661, "density": 0.7023, "total_trips": 22772137, "self_trips": 1222448, "mean_trip_distance_mi": 2.979, "gravity_beta": 1.28, "gravity_cpc": 0.796, "degree_assortativity": -0.128, "reciprocity_rho": 0.594, "weighted_reciprocity": 0.796, "modularity_Q": 0.228, "n_communities": 4, "max_kcore": 171, "global_efficiency": 0.1687, "schneider_R_random": 0.4976, "top_hubs": [ { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 976160 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 882297 }, { "zone_id": 161, "zone": "Midtown Center", "in_strength": 797677 } ] } }, "2021": { "evolution": { "year": 2021, "n_nodes": 261, "n_edges": 48451, "density": 0.714, "total_trips": 28739686, "self_trips": 1206132, "mean_trip_distance_mi": 3.247, "gravity_beta": 1.124, "gravity_cpc": 0.804, "degree_assortativity": -0.128, "reciprocity_rho": 0.61, "weighted_reciprocity": 0.791, "modularity_Q": 0.1985, "n_communities": 3, "max_kcore": 173, "global_efficiency": 0.169, "schneider_R_random": 0.4975, "top_hubs": [ { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 1274332 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 1193477 }, { "zone_id": 161, "zone": "Midtown Center", "in_strength": 955118 } ] } }, "2022": { "evolution": { "year": 2022, "n_nodes": 261, "n_edges": 42594, "density": 0.6277, "total_trips": 36838916, "self_trips": 1375869, "mean_trip_distance_mi": 3.555, "gravity_beta": 1.029, "gravity_cpc": 0.811, "degree_assortativity": -0.171, "reciprocity_rho": 0.551, "weighted_reciprocity": 0.78, "modularity_Q": 0.1758, "n_communities": 4, "max_kcore": 153, "global_efficiency": 0.1683, "schneider_R_random": 0.4974, "top_hubs": [ { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 1513617 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 1423004 }, { "zone_id": 161, "zone": "Midtown Center", "in_strength": 1367740 } ] } }, "2023": { "evolution": { "year": 2023, "n_nodes": 261, "n_edges": 43986, "density": 0.6482, "total_trips": 35521878, "self_trips": 1414091, "mean_trip_distance_mi": 3.526, "gravity_beta": 1.085, "gravity_cpc": 0.807, "degree_assortativity": -0.162, "reciprocity_rho": 0.585, "weighted_reciprocity": 0.764, "modularity_Q": 0.1954, "n_communities": 3, "max_kcore": 161, "global_efficiency": 0.1687, "schneider_R_random": 0.4985, "top_hubs": [ { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 1492371 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 1412529 }, { "zone_id": 161, "zone": "Midtown Center", "in_strength": 1392372 } ] } }, "2024": { "evolution": { "year": 2024, "n_nodes": 261, "n_edges": 49178, "density": 0.7247, "total_trips": 38041717, "self_trips": 1557978, "mean_trip_distance_mi": 3.437, "gravity_beta": 1.116, "gravity_cpc": 0.803, "degree_assortativity": -0.123, "reciprocity_rho": 0.648, "weighted_reciprocity": 0.783, "modularity_Q": 0.2064, "n_communities": 3, "max_kcore": 183, "global_efficiency": 0.1692, "schneider_R_random": 0.4982, "top_hubs": [ { "zone_id": 236, "zone": "Upper East Side North", "in_strength": 1581109 }, { "zone_id": 237, "zone": "Upper East Side South", "in_strength": 1504638 }, { "zone_id": 161, "zone": "Midtown Center", "in_strength": 1429662 } ] } } }, "scalefree": { "out_strength": { "quantity": "out_strength", "n": 262, "alpha": 1.2299, "alpha_continuous": 1.2299, "xmin": 243.0, "D": 0.0984, "n_tail": 222, "p_gof": 0.0, "powerlaw_plausible": false, "R_lognormal": 4.4864, "V_lognormal": 0.4544, "p_lognormal": 0.6495, "R_exponential": 446.8475, "V_exponential": 10.992, "p_exponential": 0.0, "LR_truncated": 60.708, "p_truncated": 0.0, "lognormal_mu": 9.8403, "lognormal_sigma": 3.1972, "verdict": "power law REJECTED by KS bootstrap (p_gof=0.000); power law NOT distinguishable from lognormal (Vuong p=0.650); CAVEAT alpha=1.23 < 2 (divergent-mean regime, pure power law strained)" }, "in_strength": { "quantity": "in_strength", "n": 262, "alpha": 1.3544, "alpha_continuous": 1.3544, "xmin": 6328.0, "D": 0.0934, "n_tail": 217, "p_gof": 0.0, "powerlaw_plausible": false, "R_lognormal": -1.1377, "V_lognormal": -0.1226, "p_lognormal": 0.9024, "R_exponential": 156.9849, "V_exponential": 6.5607, "p_exponential": 0.0, "LR_truncated": 53.2433, "p_truncated": 0.0, "lognormal_mu": 11.5746, "lognormal_sigma": 2.0066, "verdict": "power law REJECTED by KS bootstrap (p_gof=0.000); power law NOT distinguishable from lognormal (Vuong p=0.902); CAVEAT alpha=1.35 < 2 (divergent-mean regime, pure power law strained)" }, "total_strength": { "quantity": "total_strength", "n": 262, "alpha": 1.3253, "alpha_continuous": 1.3253, "xmin": 6403.0, "D": 0.087, "n_tail": 219, "p_gof": 0.0, "powerlaw_plausible": false, "R_lognormal": 4.9367, "V_lognormal": 0.532, "p_lognormal": 0.5947, "R_exponential": 232.9854, "V_exponential": 8.5402, "p_exponential": 0.0, "LR_truncated": 48.5804, "p_truncated": 0.0, "lognormal_mu": 11.8381, "lognormal_sigma": 2.266, "verdict": "power law REJECTED by KS bootstrap (p_gof=0.000); power law NOT distinguishable from lognormal (Vuong p=0.595); CAVEAT alpha=1.33 < 2 (divergent-mean regime, pure power law strained)" }, "out_degree": { "quantity": "out_degree", "n": 262, "alpha": 2.4493, "alpha_continuous": 2.4492, "xmin": 93.0, "D": 0.2194, "n_tail": 205, "p_gof": 0.0, "powerlaw_plausible": false, "R_lognormal": -74.1173, "V_lognormal": -6.2518, "p_lognormal": 0.0, "R_exponential": -47.2856, "V_exponential": -13.4364, "p_exponential": 0.0, "LR_truncated": 94.5683, "p_truncated": 0.0, "lognormal_mu": 5.2172, "lognormal_sigma": 0.3215, "verdict": "power law REJECTED by KS bootstrap (p_gof=0.000); lognormal favoured over power law (R=-74.1, p=0.000)" }, "in_degree": { "quantity": "in_degree", "n": 262, "alpha": 27.9154, "alpha_continuous": 27.8814, "xmin": 221.0, "D": 0.0599, "n_tail": 10, "p_gof": 0.998, "powerlaw_plausible": true, "R_lognormal": 1.866, "V_lognormal": 0.9805, "p_lognormal": 0.3268, "R_exponential": 0.0013, "V_exponential": 0.0061, "p_exponential": 0.9951, "LR_truncated": 0.0307, "p_truncated": 0.861, "lognormal_mu": 5.4331, "lognormal_sigma": 0.0351, "verdict": "power law plausible (p_gof=0.998); power law NOT distinguishable from lognormal (Vuong p=0.327)" }, "_meta": { "n_bootstrap": 1000, "method": "Clauset-Shalizi-Newman discrete MLE; Vuong LR vs lognormal/exponential; nested LR vs truncated PL", "powerlaw_package_available": false, "n_nodes": 262, "note": "Strength distributions are the scientifically central quantities; degree distributions are structurally truncated by N-1 so a clean power law is impossible there. Short tail (262 nodes) limits power to distinguish power law from lognormal." } }, "null_models": { "graph": { "nodes": 262, "edges": 42347, "density": 0.6193 }, "n_null_graphs": 100, "observed": { "transitivity": 0.83302, "assortativity": -0.184, "reciprocity_gl": 0.51491, "weighted_reciprocity": 0.81752, "efficiency_unweighted": 0.808, "efficiency_cost": 4030.62128 }, "erdos_renyi": { "transitivity": { "observed": 0.83302, "null_mean": 0.8548, "null_std": 0.00123, "z": -17.772, "percentile": 0.0 }, "assortativity": { "observed": -0.184, "null_mean": -0.00328, "null_std": 0.00294, "z": -61.447, "percentile": 0.0 }, "reciprocity_gl": { "observed": 0.51491, "null_mean": 0.00098, "null_std": 0.00516, "z": 99.517, "percentile": 1.0 }, "efficiency_unweighted": { "observed": 0.808, "null_mean": 0.80964, "null_std": 0.0, "z": null, "percentile": 0.0 } }, "configuration": { "transitivity": { "observed": 0.83302, "null_mean": 0.71626, "null_std": 0.00162, "z": 72.157, "percentile": 1.0 }, "assortativity": { "observed": -0.184, "null_mean": -0.02871, "null_std": 0.00482, "z": -32.22, "percentile": 0.0 }, "reciprocity_gl": { "observed": 0.51491, "null_mean": 0.10651, "null_std": 0.00491, "z": 83.214, "percentile": 1.0 }, "efficiency_unweighted": { "observed": 0.808, "null_mean": 0.71293, "null_std": 0.00048, "z": 198.519, "percentile": 1.0 } }, "configuration_meta": { "observed_edges": 42347, "simplified_null_edges_mean": 29275.0, "edge_loss_pct_to_simplification": 30.87 }, "weight_preserving": { "weighted_reciprocity": { "observed": 0.81752, "null_mean": 0.04361, "null_std": 0.00356, "z": 217.18, "percentile": 1.0 }, "efficiency_cost": { "observed": 4030.62128, "null_mean": 21605.85284, "null_std": 325.21947, "z": -54.041, "percentile": 0.0 } }, "degeneracy_note": "At density 0.62 the observed topology is near-complete, so the ER and directed-configuration nulls reproduce observed transitivity and the near-zero assortativity almost exactly - their z-scores are uninformative (transitivity is structurally forced; assortativity hovers at 0). The WEIGHT-PRESERVING null is the decisive comparison: topology and degrees are held exactly, only the weight-topology coupling is destroyed, so a nonzero z on weighted reciprocity / cost-weighted efficiency reports genuine flow/spatial organisation (heavy flows sit on mutual high-volume corridors), not a topological artefact." }, "spatial": { "n_nodes": 262, "n_edges": 42347, "n_nodes_without_geometry": 3, "efficiency": { "n_nodes_geo": 259, "E_glob_distance": 0.17291, "E_glob_ideal_complete_spatial": 0.17347, "E_glob_normalized": 0.9968, "E_loc_distance": 0.22077, "E_glob_flowcost": 4122.269858, "note": "distance weight = Euclidean miles between EPSG:2263 centroids; ideal = complete graph with straight-line edges (Barthelemy); flow-cost weight = 1/trips." }, "circuity": { "n_pairs": 66822, "mean_circuity": 1.0061, "median_circuity": 1.0, "p90_circuity": 1.002, "max_circuity": 23.156, "mean_straightness_centrality": 0.9968, "most_circuitous_corridors": [ { "o": "Oakwood", "d": "Great Kills Park", "circuity": 23.156, "straight_mi": 1.16 }, { "o": "Great Kills", "d": "Great Kills Park", "circuity": 22.63, "straight_mi": 1.26 }, { "o": "New Dorp/Midland Beach", "d": "Great Kills Park", "circuity": 11.857, "straight_mi": 2.17 }, { "o": "Arden Heights", "d": "Great Kills Park", "circuity": 9.217, "straight_mi": 3.2 }, { "o": "Eltingville/Annadale/Prince's Bay", "d": "Great Kills Park", "circuity": 9.188, "straight_mi": 3.34 }, { "o": "Heartland Village/Todt Hill", "d": "Great Kills Park", "circuity": 9.122, "straight_mi": 2.82 }, { "o": "Freshkills Park", "d": "Great Kills Park", "circuity": 7.887, "straight_mi": 3.73 }, { "o": "Rossville/Woodrow", "d": "Great Kills Park", "circuity": 7.339, "straight_mi": 4.2 } ], "note": "Q = network shortest-path distance / straight-line distance (>=1); corridors filtered to straight-line >= 0.5 mi so tiny adjacent pairs do not dominate the ratio." }, "betweenness_spatial_autocorrelation": { "load_gini": 0.8896, "top10_betweenness_share": 0.5469, "moran": { "morans_I": 0.0278, "expected_I": -0.00388, "p_value_perm": 0.238, "n_permutations": 999, "k_neighbours": 6 } }, "cascade": { "trigger_node": 132, "trigger_zone": "JFK Airport", "trigger_load_rank": "highest flow-cost betweenness", "load_gini": 0.8896, "n_zero_load_nodes": 149, "tolerances": [ 0.05, 0.1, 0.2, 0.3, 0.5, 1.0 ], "G_alpha_curve": [ { "alpha": 0.05, "G": 0.2548, "cascade_fraction": 0.7413, "surviving_flow_fraction": 0.008 }, { "alpha": 0.1, "G": 0.2934, "cascade_fraction": 0.7027, "surviving_flow_fraction": 0.0081 }, { "alpha": 0.2, "G": 0.2819, "cascade_fraction": 0.7143, "surviving_flow_fraction": 0.0087 }, { "alpha": 0.3, "G": 0.4981, "cascade_fraction": 0.5019, "surviving_flow_fraction": 0.0651 }, { "alpha": 0.5, "G": 0.5444, "cascade_fraction": 0.4556, "surviving_flow_fraction": 0.1137 }, { "alpha": 1.0, "G": 0.7722, "cascade_fraction": 0.2278, "surviving_flow_fraction": 0.2015 } ], "alpha_no_collapse": null, "no_collapse_criterion": "smallest alpha with surviving giant WCC >= 0.80 N0", "note": "synchronous update; capacity fixed at (1+alpha)*load0; load = unnormalized flow-cost betweenness recomputed each step. Most nodes carry ~0 load (see load_gini / n_zero_load_nodes) so the cascade is hub-driven. Failed nodes labelled injector/absorber by net_flow_index sign (Peterson-Rajan). CAVEAT: the n_zero_load_nodes zero-initial-load nodes have capacity exactly (1+alpha)*0 = 0, so the moment any flow reroutes through one post-trigger it overloads and fails on any alpha; the 'alpha_no_collapse=None' conclusion is therefore partly a zero-capacity artifact of peripheral nodes, not purely hub fragility." } }, "robustness": { "n_nodes": 262, "n_edges": 42347, "total_trips": 135738831.0, "efficiency_E0": 4030.621281741512, "molloy_reed_kappa": 365.45283018867923, "n_random_seeds": 100, "n_random_seeds_efficiency": 20, "fractions": [ 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12, 0.14, 0.16, 0.18, 0.2, 0.22, 0.24, 0.26, 0.28, 0.3, 0.32, 0.34, 0.36, 0.38, 0.4, 0.42, 0.44, 0.46, 0.48, 0.5, 0.52, 0.54, 0.56, 0.58, 0.6 ], "schneider_R_wcc": { "random": 0.6999507510465404, "strength": 0.7000738734301895, "strength_recomp": 0.7000738734301895, "betweenness": 0.6992120167446442, "pagerank": 0.7000738734301895 }, "schneider_R_scc": { "random": 0.698640728884511, "strength": 0.6947796109332676, "strength_recomp": 0.6953952228515143, "betweenness": 0.6951489780842157, "pagerank": 0.6960108347697611 }, "critical_f_wcc": { "random": 0.5, "strength": 0.52, "strength_recomp": 0.52, "betweenness": 0.52, "pagerank": 0.52 }, "critical_f_trip": { "random": 0.32, "strength": 0.04, "strength_recomp": 0.04, "betweenness": 0.08, "pagerank": 0.04 }, "attack_vs_failure_gap": { "probe_fraction": 0.1, "random_trip_frac": 0.8221799081207647, "worst_attack_strategy": "strength_recomp", "worst_attack_trip_frac": 0.12977328499314983, "trip_frac_gap": 0.6924066231276149, "random_eff_frac": 0.9606312306639591, "worst_attack_eff_frac": 0.1733959960768358 }, "recompute_note": "strength attack run both static and recomputed; betweenness/pagerank static only (all-pairs betweenness per step is the sole costly piece).", "weighting_note": "efficiency uses weight=cost=1/trips (flow-resistance Dijkstra); trip_frac counts trips inside the giant WCC." } }