Ranking football clubs by the dominant eigenvector of the normalized points-won matrix.
South America 2021
| ‹ 2020 | History | 2022 › |
|---|---|---|
| EP | Pts | W | D | L | GF | GA | GP | PR | ||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Atlético Mineiro | 4.352 | 129 | 38 | 15 | 8 | 105 | 49 | 61 | 1 |
| 2 | Flamengo | 4.002 | 123 | 37 | 12 | 14 | 124 | 63 | 63 | 2 |
| 3 | Bragantino | 2.724 | 106 | 29 | 19 | 14 | 94 | 67 | 62 | 5 |
| 4 | Palmeiras | 2.605 | 119 | 35 | 14 | 19 | 108 | 70 | 68 | 3 |
| 5 | Fluminense | 2.437 | 97 | 27 | 16 | 16 | 72 | 59 | 59 | 10 |
| 6 | River Plate | 2.119 | 71 | 20 | 11 | 8 | 67 | 38 | 39 | 33 |
| 7 | Atlético Goianiense | 1.987 | 79 | 19 | 22 | 14 | 52 | 51 | 55 | 26 |
| 8 | Athletico Paranaense | 1.870 | 99 | 29 | 12 | 21 | 77 | 59 | 62 | 7 |
| 9 | Ceará | 1.862 | 75 | 18 | 21 | 16 | 60 | 54 | 55 | 29 |
| 10 | Defensa y Justicia | 1.845 | 67 | 18 | 13 | 9 | 69 | 49 | 40 | 40 |
| 11 | Santos | 1.771 | 90 | 23 | 21 | 22 | 72 | 74 | 66 | 15 |
| 12 | Internacional | 1.648 | 83 | 22 | 17 | 18 | 76 | 56 | 57 | 17 |
| 13 | Talleres de Córdoba | 1.575 | 60 | 18 | 6 | 9 | 50 | 36 | 33 | 58 |
| 14 | Boca Juniors | 1.478 | 57 | 14 | 15 | 9 | 46 | 29 | 38 | 65 |
| 15 | Corinthians | 1.403 | 79 | 21 | 16 | 18 | 67 | 57 | 55 | 25 |
| 16 | Fortaleza | 1.402 | 68 | 20 | 8 | 21 | 54 | 64 | 49 | 39 |
| 17 | Grêmio Porto Alegre | 1.364 | 82 | 23 | 13 | 26 | 95 | 82 | 62 | 20 |
| 18 | Independiente | 1.364 | 56 | 15 | 11 | 9 | 44 | 35 | 35 | 68 |
| 19 | América Mineiro | 1.345 | 53 | 13 | 14 | 11 | 41 | 37 | 38 | 73 |
| 20 | Vélez Sarsfield | 1.220 | 61 | 17 | 10 | 11 | 53 | 39 | 38 | 56 |
| 21 | São Paulo | 1.220 | 74 | 17 | 23 | 19 | 57 | 66 | 59 | 30 |
| 22 | Peñarol | 1.217 | 116 | 32 | 20 | 8 | 98 | 47 | 60 | 4 |
| 23 | Cuiabá | 1.211 | 47 | 10 | 17 | 11 | 34 | 37 | 38 | 97 |
| 24 | Emelec | 1.179 | 79 | 23 | 10 | 7 | 74 | 43 | 40 | 23 |
| 25 | Lanús | 1.137 | 57 | 16 | 9 | 11 | 59 | 53 | 36 | 66 |
| 26 | Bahia | 1.132 | 67 | 17 | 16 | 22 | 68 | 70 | 55 | 41 |
| 27 | Independiente del Valle | 1.102 | 80 | 23 | 11 | 10 | 79 | 48 | 44 | 22 |
| 28 | Juventude | 1.091 | 46 | 11 | 13 | 14 | 36 | 44 | 38 | 101 |
| 29 | Colón de Santa Fe | 0.993 | 42 | 12 | 6 | 9 | 29 | 33 | 27 | 109 |
| 30 | Argentinos Juniors | 0.904 | 49 | 13 | 10 | 12 | 37 | 33 | 35 | 95 |
| 31 | Estudiantes | 0.896 | 39 | 10 | 9 | 8 | 44 | 34 | 27 | 118 |
| 32 | Gimnasia de La Plata | 0.883 | 39 | 10 | 9 | 8 | 29 | 30 | 27 | 120 |
| 33 | Huracán | 0.859 | 38 | 10 | 8 | 9 | 28 | 27 | 27 | 127 |
| 34 | LDU Quito | 0.852 | 62 | 16 | 14 | 10 | 69 | 60 | 40 | 51 |
| 35 | Nacional | 0.845 | 101 | 29 | 14 | 13 | 79 | 56 | 56 | 6 |
| 36 | Barcelona SC | 0.830 | 69 | 20 | 9 | 13 | 67 | 45 | 42 | 36 |
| 37 | Atlético Nacional | 0.812 | 97 | 27 | 16 | 13 | 96 | 51 | 56 | 8 |
| 38 | Godoy Cruz | 0.811 | 34 | 9 | 7 | 11 | 38 | 36 | 27 | 140 |
| 39 | Racing Club | 0.785 | 51 | 13 | 12 | 10 | 40 | 32 | 35 | 80 |
| 40 | Atlético Junior | 0.784 | 95 | 24 | 23 | 13 | 80 | 61 | 60 | 11 |
| 41 | Sport Recife | 0.778 | 51 | 13 | 12 | 24 | 32 | 51 | 49 | 86 |
| 42 | Newell's Old Boys | 0.728 | 36 | 9 | 9 | 15 | 31 | 42 | 33 | 136 |
| 43 | Montevideo City Torque | 0.713 | 94 | 27 | 13 | 14 | 101 | 60 | 54 | 12 |
| 44 | Platense | 0.678 | 31 | 7 | 10 | 8 | 36 | 36 | 25 | 151 |
| 45 | Rosario Central | 0.677 | 50 | 14 | 8 | 16 | 59 | 56 | 38 | 89 |
| 46 | Banfield | 0.670 | 31 | 6 | 13 | 9 | 27 | 30 | 28 | 153 |
| 47 | Plaza Colonia | 0.666 | 82 | 23 | 13 | 10 | 69 | 42 | 46 | 19 |
| 48 | Aldosivi | 0.654 | 34 | 10 | 4 | 13 | 34 | 46 | 27 | 142 |
| 49 | Vasco da Gama | 0.649 | 13 | 3 | 4 | 5 | 11 | 17 | 12 | 181 |
| 50 | Goiás | 0.647 | 14 | 4 | 2 | 5 | 14 | 21 | 11 | 180 |
| 51 | Always Ready | 0.638 | 71 | 21 | 8 | 7 | 74 | 42 | 36 | 32 |
| 52 | Arsenal de Sarandí | 0.637 | 39 | 9 | 12 | 14 | 28 | 44 | 35 | 124 |
| 53 | Libertad | 0.633 | 91 | 27 | 10 | 15 | 89 | 57 | 52 | 14 |
| 54 | Liverpool | 0.633 | 80 | 23 | 11 | 14 | 90 | 57 | 48 | 21 |
| 55 | Alianza Lima | 0.627 | 60 | 17 | 9 | 2 | 40 | 17 | 28 | 57 |
| 56 | Universidad Catolica | 0.618 | 58 | 16 | 10 | 8 | 60 | 38 | 34 | 63 |
| 57 | San Lorenzo | 0.599 | 39 | 10 | 9 | 18 | 38 | 51 | 37 | 123 |
| 58 | Unión de Santa Fe | 0.594 | 37 | 11 | 4 | 12 | 36 | 35 | 27 | 130 |
| 59 | Universidad Católica | 0.593 | 93 | 29 | 6 | 15 | 84 | 52 | 50 | 13 |
| 60 | Deportes Tolima | 0.584 | 97 | 24 | 25 | 11 | 76 | 49 | 60 | 9 |
| 61 | Central Córdoba SdE | 0.583 | 30 | 7 | 9 | 11 | 34 | 39 | 27 | 157 |
| 62 | Millonarios | 0.571 | 88 | 26 | 10 | 14 | 78 | 53 | 50 | 16 |
| 63 | Patronato de Paraná | 0.552 | 29 | 6 | 11 | 10 | 26 | 37 | 27 | 159 |
| 64 | Deportivo Cali | 0.518 | 83 | 22 | 17 | 11 | 62 | 49 | 50 | 18 |
| 65 | 9 de Octubre | 0.514 | 50 | 15 | 5 | 10 | 47 | 38 | 30 | 87 |
| 66 | Atlético Tucumán | 0.484 | 25 | 6 | 7 | 14 | 23 | 48 | 27 | 168 |
| 67 | Cerro Largo | 0.479 | 64 | 16 | 16 | 15 | 62 | 56 | 47 | 47 |
| 68 | The Strongest | 0.478 | 69 | 21 | 6 | 9 | 61 | 38 | 36 | 35 |
| 69 | Colo-Colo | 0.474 | 79 | 23 | 10 | 9 | 57 | 33 | 42 | 24 |
| 70 | Coritiba | 0.442 | 10 | 2 | 4 | 5 | 10 | 17 | 11 | 187 |
| 71 | Sarmiento de Junín | 0.418 | 24 | 6 | 6 | 13 | 23 | 33 | 25 | 170 |
| 72 | Independiente Petrolero | 0.414 | 65 | 20 | 5 | 5 | 59 | 33 | 30 | 44 |
| 73 | La Equidad | 0.400 | 60 | 15 | 15 | 12 | 46 | 44 | 42 | 60 |
| 74 | Montevideo Wanderers | 0.382 | 66 | 18 | 12 | 18 | 60 | 67 | 48 | 43 |
| 75 | Audax Italiano | 0.376 | 66 | 17 | 15 | 8 | 50 | 40 | 40 | 42 |
| 76 | Bolívar | 0.372 | 68 | 19 | 11 | 10 | 75 | 42 | 40 | 38 |
| 77 | Santa Fe | 0.366 | 62 | 15 | 17 | 14 | 51 | 46 | 46 | 52 |
| 78 | Aucas | 0.362 | 51 | 14 | 9 | 15 | 59 | 55 | 38 | 81 |
| 79 | River Plate Montevidio | 0.357 | 63 | 17 | 12 | 16 | 66 | 64 | 45 | 48 |
| 80 | Sporting Cristal | 0.353 | 70 | 21 | 7 | 11 | 66 | 46 | 39 | 34 |
| 81 | Chapecoense | 0.348 | 15 | 1 | 12 | 25 | 27 | 67 | 38 | 178 |
| 82 | Atlético Bucaramanga | 0.345 | 51 | 13 | 12 | 13 | 46 | 45 | 38 | 82 |
| 83 | Boston River | 0.334 | 59 | 16 | 11 | 19 | 62 | 71 | 46 | 62 |
| 84 | Fénix | 0.330 | 62 | 15 | 17 | 15 | 62 | 68 | 47 | 55 |
| 85 | Deportivo Táchira | 0.327 | 78 | 23 | 9 | 11 | 83 | 53 | 43 | 27 |
| 86 | Cerro Porteño | 0.319 | 76 | 22 | 10 | 12 | 55 | 38 | 44 | 28 |
| 87 | Delfín SC | 0.316 | 40 | 10 | 10 | 10 | 44 | 45 | 30 | 114 |
| 88 | Independiente Medellín | 0.308 | 52 | 11 | 19 | 8 | 31 | 30 | 38 | 75 |
| 89 | Deportivo Maldonado | 0.305 | 49 | 12 | 13 | 20 | 45 | 67 | 45 | 96 |
| 90 | Técnico Universitario | 0.293 | 35 | 8 | 11 | 11 | 24 | 26 | 30 | 138 |
| 91 | América de Cali | 0.292 | 69 | 18 | 15 | 21 | 57 | 56 | 54 | 37 |
| 92 | Jaguares de Córdoba | 0.291 | 52 | 14 | 10 | 14 | 44 | 47 | 38 | 77 |
| 93 | Macará | 0.290 | 37 | 9 | 10 | 13 | 37 | 50 | 32 | 132 |
| 94 | Defensor Sporting | 0.286 | 15 | 2 | 9 | 5 | 16 | 22 | 16 | 176 |
| 95 | Unión La Calera | 0.280 | 65 | 18 | 11 | 20 | 68 | 73 | 49 | 46 |
| 96 | Cerrito | 0.275 | 40 | 11 | 7 | 12 | 34 | 37 | 30 | 115 |
| 97 | Club Olimpia | 0.273 | 62 | 19 | 5 | 22 | 73 | 75 | 46 | 53 |
| 98 | FBC Melgar | 0.272 | 56 | 16 | 8 | 10 | 57 | 35 | 34 | 67 |
| 99 | Universitario de Deportes | 0.270 | 51 | 14 | 9 | 9 | 49 | 49 | 32 | 83 |
| 100 | Deportivo Pereira | 0.270 | 56 | 14 | 14 | 16 | 46 | 58 | 44 | 70 |
| 101 | Mushuc Runa | 0.268 | 41 | 11 | 8 | 11 | 41 | 42 | 30 | 112 |
| 102 | Unión Española | 0.264 | 58 | 17 | 7 | 19 | 63 | 76 | 43 | 64 |
| 103 | Jorge Wilstermann | 0.263 | 60 | 18 | 6 | 14 | 73 | 60 | 38 | 59 |
| 104 | Progreso | 0.255 | 51 | 13 | 12 | 20 | 39 | 57 | 45 | 85 |
| 105 | Ñublense | 0.250 | 44 | 11 | 11 | 10 | 49 | 37 | 32 | 104 |
| 106 | Universidad de Chile | 0.250 | 56 | 14 | 14 | 15 | 47 | 45 | 43 | 69 |
| 107 | Guaraní | 0.241 | 65 | 18 | 11 | 11 | 68 | 53 | 40 | 45 |
| 108 | Palestino | 0.240 | 62 | 16 | 14 | 19 | 71 | 74 | 49 | 54 |
| 109 | O'Higgins | 0.237 | 52 | 12 | 16 | 13 | 41 | 47 | 41 | 78 |
| 110 | Huachipato | 0.235 | 63 | 16 | 15 | 17 | 58 | 63 | 48 | 49 |
| 111 | Antofagasta | 0.232 | 55 | 14 | 13 | 15 | 43 | 53 | 42 | 72 |
| 112 | Deportivo Cuenca | 0.230 | 32 | 8 | 8 | 14 | 39 | 42 | 30 | 146 |
| 113 | Caracas FC | 0.225 | 71 | 20 | 11 | 8 | 76 | 42 | 39 | 31 |
| 114 | Orense SC | 0.221 | 31 | 7 | 10 | 13 | 28 | 37 | 30 | 155 |
| 115 | Club Nacional | 0.211 | 52 | 12 | 16 | 10 | 43 | 44 | 38 | 76 |
| 116 | Envigado FC | 0.210 | 44 | 10 | 14 | 14 | 39 | 46 | 38 | 106 |
| 117 | Rentistas | 0.209 | 44 | 10 | 14 | 31 | 46 | 88 | 55 | 107 |
| 118 | Everton | 0.205 | 50 | 13 | 11 | 16 | 36 | 45 | 40 | 91 |
| 119 | Cienciano | 0.200 | 39 | 10 | 9 | 7 | 39 | 33 | 26 | 119 |
| 120 | Deportivo Pasto | 0.198 | 42 | 9 | 15 | 16 | 34 | 51 | 40 | 111 |
| 121 | Cobresal | 0.195 | 55 | 15 | 10 | 18 | 55 | 51 | 43 | 71 |
| 122 | Oriente Petrolero | 0.194 | 51 | 15 | 6 | 9 | 46 | 29 | 30 | 79 |
| 123 | 12 de Octubre de Itauguá | 0.189 | 51 | 11 | 18 | 15 | 41 | 52 | 44 | 84 |
| 124 | Danubio | 0.186 | 15 | 4 | 3 | 8 | 17 | 23 | 15 | 175 |
| 125 | Royal Pari | 0.183 | 52 | 16 | 4 | 12 | 68 | 50 | 32 | 74 |
| 126 | CA Cerro | 0.183 | 14 | 3 | 5 | 7 | 16 | 21 | 15 | 179 |
| 127 | Manta | 0.181 | 28 | 6 | 10 | 14 | 29 | 46 | 30 | 161 |
| 128 | Monagas | 0.180 | 62 | 18 | 8 | 8 | 58 | 39 | 34 | 50 |
| 129 | La Serena | 0.172 | 47 | 10 | 17 | 14 | 48 | 54 | 41 | 98 |
| 130 | Boyacá Chicó | 0.171 | 19 | 5 | 4 | 9 | 17 | 20 | 18 | 174 |
| 131 | Once Caldas | 0.170 | 37 | 8 | 13 | 17 | 38 | 53 | 38 | 134 |
| 132 | Deportes Quindío | 0.167 | 22 | 6 | 4 | 10 | 18 | 24 | 20 | 172 |
| 133 | Curicó Unido | 0.166 | 46 | 10 | 16 | 16 | 49 | 58 | 42 | 102 |
| 134 | River Plate Asunción | 0.164 | 45 | 11 | 12 | 21 | 40 | 73 | 44 | 103 |
| 135 | Sud América | 0.160 | 31 | 8 | 7 | 15 | 29 | 48 | 30 | 156 |
| 136 | Melipilla | 0.158 | 38 | 10 | 8 | 14 | 39 | 51 | 32 | 129 |
| 137 | Universidad Cesar Vallejo | 0.155 | 43 | 11 | 10 | 7 | 31 | 22 | 28 | 108 |
| 138 | Guaireña FC | 0.155 | 44 | 10 | 14 | 14 | 35 | 41 | 38 | 105 |
| 139 | Alianza Petrolera | 0.154 | 41 | 9 | 14 | 21 | 43 | 70 | 44 | 113 |
| 140 | Rionegro Águilas Doradas | 0.147 | 39 | 9 | 12 | 17 | 37 | 49 | 38 | 122 |
| 141 | Deportivo La Guaira | 0.139 | 50 | 12 | 14 | 14 | 43 | 51 | 40 | 90 |
| 142 | Guayaquil City | 0.139 | 30 | 8 | 6 | 18 | 28 | 53 | 32 | 158 |
| 143 | Patriotas FC | 0.138 | 35 | 9 | 8 | 21 | 31 | 52 | 38 | 139 |
| 144 | Sol de América | 0.134 | 42 | 11 | 9 | 16 | 40 | 50 | 36 | 110 |
| 145 | Deportivo Lara | 0.129 | 46 | 10 | 16 | 10 | 54 | 42 | 36 | 100 |
| 146 | Real Santa Cruz | 0.125 | 38 | 11 | 5 | 14 | 39 | 47 | 30 | 128 |
| 147 | Sport Boys | 0.123 | 38 | 10 | 8 | 8 | 36 | 34 | 26 | 126 |
| 148 | Metropolitanos FC | 0.120 | 59 | 16 | 11 | 13 | 60 | 51 | 40 | 61 |
| 149 | Mannucci | 0.119 | 36 | 10 | 6 | 12 | 43 | 45 | 28 | 135 |
| 150 | CD Guabirá | 0.117 | 50 | 15 | 5 | 18 | 54 | 67 | 38 | 92 |
| 151 | Botafogo | 0.115 | 4 | 1 | 1 | 9 | 7 | 23 | 11 | 190 |
| 152 | Sportivo Luqueño | 0.114 | 39 | 10 | 9 | 17 | 35 | 56 | 36 | 125 |
| 153 | Sport Huancayo | 0.113 | 37 | 8 | 13 | 13 | 34 | 47 | 34 | 133 |
| 154 | Iquique | 0.107 | 11 | 2 | 5 | 3 | 12 | 13 | 10 | 183 |
| 155 | Ayacucho FC | 0.105 | 37 | 9 | 10 | 9 | 39 | 44 | 28 | 131 |
| 156 | Nacional Potosí | 0.104 | 39 | 10 | 9 | 13 | 47 | 52 | 32 | 121 |
| 157 | Atlético Palmaflor | 0.102 | 40 | 11 | 7 | 14 | 44 | 49 | 32 | 116 |
| 158 | Universidad de Concepción | 0.099 | 10 | 2 | 4 | 2 | 8 | 9 | 8 | 184 |
| 159 | Deportivo Municipal | 0.097 | 31 | 9 | 4 | 13 | 32 | 37 | 26 | 154 |
| 160 | Santiago Wanderers | 0.092 | 32 | 8 | 8 | 24 | 32 | 65 | 40 | 149 |
| 161 | Hermanos Colmenarez | 0.089 | 49 | 12 | 13 | 7 | 56 | 44 | 32 | 94 |
| 162 | Estudiantes de Mérida | 0.088 | 50 | 14 | 8 | 12 | 51 | 47 | 34 | 88 |
| 163 | Coquimbo Unido | 0.086 | 10 | 2 | 4 | 5 | 12 | 14 | 11 | 185 |
| 164 | Cusco FC | 0.081 | 26 | 6 | 8 | 12 | 43 | 47 | 26 | 163 |
| 165 | Universidad Técnica | 0.080 | 33 | 9 | 6 | 13 | 28 | 38 | 28 | 144 |
| 166 | Villa Española | 0.077 | 15 | 2 | 9 | 19 | 26 | 60 | 30 | 177 |
| 167 | Portuguesa FC | 0.076 | 49 | 13 | 10 | 9 | 41 | 28 | 32 | 93 |
| 168 | Club Aurora | 0.076 | 33 | 9 | 6 | 15 | 40 | 51 | 30 | 145 |
| 169 | Real Tomayapo | 0.075 | 32 | 9 | 5 | 16 | 28 | 45 | 30 | 148 |
| 170 | Aragua FC | 0.072 | 47 | 11 | 14 | 15 | 38 | 57 | 40 | 99 |
| 171 | Academia Cantolao | 0.068 | 27 | 7 | 6 | 13 | 28 | 37 | 26 | 162 |
| 172 | Atlético Huila | 0.066 | 10 | 2 | 4 | 14 | 12 | 35 | 20 | 188 |
| 173 | Alianza Atlético | 0.061 | 25 | 7 | 4 | 15 | 31 | 46 | 26 | 166 |
| 174 | Blooming | 0.060 | 26 | 7 | 5 | 18 | 34 | 56 | 30 | 164 |
| 175 | Real Potosí | 0.060 | 25 | 7 | 4 | 19 | 30 | 63 | 30 | 169 |
| 176 | Alianza Universidad | 0.060 | 24 | 6 | 6 | 14 | 25 | 45 | 26 | 171 |
| 177 | Olmedo | 0.059 | 13 | 2 | 7 | 21 | 22 | 76 | 30 | 182 |
| 178 | Deportivo Binacional | 0.054 | 25 | 7 | 4 | 15 | 32 | 50 | 26 | 167 |
| 179 | Zamora FC | 0.052 | 35 | 9 | 8 | 7 | 38 | 28 | 24 | 137 |
| 180 | Universidad San Martín | 0.051 | 26 | 7 | 5 | 15 | 18 | 41 | 27 | 165 |
| 181 | Atlético Venezuela | 0.049 | 34 | 9 | 7 | 8 | 36 | 38 | 24 | 141 |
| 182 | Academia Puerto Cabello | 0.048 | 40 | 9 | 13 | 12 | 34 | 39 | 34 | 117 |
| 183 | GV Maracay | 0.041 | 33 | 8 | 9 | 7 | 25 | 32 | 24 | 143 |
| 184 | Mineros de Guayana | 0.041 | 32 | 9 | 5 | 12 | 27 | 35 | 26 | 147 |
| 185 | Carabobo FC | 0.039 | 31 | 8 | 7 | 9 | 28 | 28 | 24 | 152 |
| 186 | Universidad Central | 0.037 | 31 | 8 | 7 | 9 | 32 | 30 | 24 | 150 |
| 187 | Internacional de Bogotá | 0.035 | 10 | 3 | 1 | 4 | 9 | 11 | 8 | 186 |
| 188 | Zulia FC | 0.033 | 28 | 7 | 7 | 10 | 35 | 34 | 24 | 160 |
| 189 | Yaracuyanos FC | 0.023 | 20 | 5 | 5 | 14 | 16 | 32 | 24 | 173 |
| 190 | LALA FC | 0.015 | 9 | 2 | 3 | 19 | 15 | 58 | 24 | 189 |
| 191 | Trujillanos FC | 0.001 | 1 | 0 | 1 | 23 | 8 | 79 | 24 | 191 |
| 192 | San José | 0.001 | 1 | 0 | 1 | 29 | 9 | 96 | 30 | 192 |
EigenPoints, Points, Wins, Draws, Losses, GoalsFor, GoalsAgainst, GamesPlayed, PointsRank.
| « 2007 | History | 2026 » |
|---|
Includes matches from Copa Libertadores, Copa Sudamericana, Recopa Sudamericana, and the top domestic divisions of participating countries played during the calendar year.
Matches decided on penalties are treated as ties.