task
class label 5
classes | type
class label 2
classes | prompt
stringlengths 298
1.22k
| input
stringclasses 10
values | output
stringlengths 3
6
|
|---|---|---|---|---|
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 3), (0, 6), (0, 10), (0, 13), (1, 2), (1, 3), (1, 5), (1, 7), (1, 10), (1, 13), (1, 15), (2, 4), (2, 6), (2, 7), (2, 9), (2, 14), (4, 7), (4, 12), (4, 13), (4, 14), (5, 7), (5, 12), (5, 15), (6, 7), (6, 9), (6, 11), (6, 15), (7, 11), (7, 12), (7, 13), (7, 14), (8, 12), (8, 14), (8, 15), (9, 13), (9, 14), (10, 11), (10, 13), (11, 12), (11, 13), (11, 15), (12, 14), (12, 15), (13, 14), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 3), (0, 5), (0, 6), (0, 7), (1, 2), (1, 11), (1, 13), (2, 3), (2, 6), (2, 10), (2, 11), (2, 13), (2, 14), (3, 8), (3, 15), (4, 8), (4, 11), (4, 15), (5, 6), (5, 8), (5, 9), (6, 10), (6, 14), (8, 13), (8, 14), (9, 10), (9, 15), (10, 12), (10, 13), (11, 12), (11, 14), (13, 15), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 5), (0, 14), (1, 8), (1, 10), (2, 4), (2, 7), (2, 17), (2, 18), (4, 5), (4, 17), (6, 11), (9, 10), (10, 13), (13, 18), (14, 17), (15, 18), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "5" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 1), (0, 3), (0, 10), (0, 12), (0, 13), (0, 15), (0, 16), (1, 4), (1, 6), (1, 9), (1, 10), (1, 12), (1, 13), (1, 14), (2, 3), (2, 4), (2, 5), (2, 7), (2, 8), (2, 13), (2, 14), (2, 15), (2, 16), (3, 5), (3, 8), (3, 10), (3, 11), (3, 15), (3, 16), (4, 6), (4, 7), (4, 12), (4, 13), (4, 17), (5, 10), (5, 11), (5, 13), (5, 14), (5, 16), (5, 17), (6, 9), (6, 10), (6, 11), (6, 13), (6, 14), (6, 15), (6, 17), (7, 16), (8, 9), (8, 11), (8, 13), (8, 14), (8, 17), (9, 13), (9, 15), (9, 17), (10, 14), (10, 15), (11, 17), (12, 15), (12, 17), (13, 15), (13, 16), (14, 15), (14, 16), (15, 16), (16, 17), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 1), (0, 7), (0, 15), (0, 17), (1, 2), (1, 4), (1, 6), (1, 8), (1, 12), (1, 13), (1, 15), (2, 4), (2, 13), (3, 6), (3, 13), (3, 16), (3, 17), (4, 7), (4, 16), (5, 6), (5, 7), (5, 12), (5, 15), (6, 15), (7, 8), (7, 9), (7, 10), (7, 11), (7, 13), (7, 14), (7, 15), (8, 10), (8, 13), (8, 14), (9, 14), (10, 12), (11, 12), (11, 14), (12, 18), (14, 17), (14, 18), (16, 17), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 7), (1, 4), (1, 9), (2, 4), (5, 10), (8, 10), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "5" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 2), (0, 3), (0, 7), (1, 2), (1, 8), (2, 3), (2, 6), (2, 7), (2, 10), (2, 11), (3, 4), (3, 6), (4, 5), (4, 7), (4, 10), (4, 11), (5, 11), (6, 9), (6, 11), (7, 9), (7, 11), (7, 12), (8, 9), (8, 12), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 1), (0, 3), (0, 8), (0, 9), (1, 2), (1, 5), (1, 10), (2, 6), (2, 9), (3, 4), (3, 6), (3, 7), (5, 10), (6, 7), (6, 9), (9, 10), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 2), (0, 11), (0, 15), (1, 3), (2, 14), (3, 6), (4, 5), (4, 7), (4, 15), (5, 8), (6, 9), (7, 13), (9, 10), (10, 12), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 1), (0, 2), (0, 4), (0, 5), (0, 6), (0, 9), (0, 12), (0, 13), (0, 18), (1, 2), (1, 7), (1, 15), (2, 3), (2, 6), (2, 7), (2, 8), (2, 11), (2, 12), (2, 15), (3, 8), (3, 10), (3, 13), (3, 18), (4, 6), (4, 10), (4, 11), (4, 12), (4, 15), (4, 16), (4, 18), (5, 6), (5, 7), (5, 10), (5, 15), (6, 7), (6, 9), (6, 13), (6, 14), (6, 16), (6, 17), (7, 8), (7, 12), (7, 16), (8, 9), (8, 14), (8, 18), (9, 11), (9, 18), (10, 11), (10, 12), (10, 13), (10, 14), (10, 15), (10, 16), (11, 12), (11, 14), (11, 17), (11, 18), (12, 13), (12, 15), (12, 18), (13, 15), (13, 16), (13, 18), (14, 16), (14, 17), (14, 18), (15, 16), (15, 17), (15, 18), (16, 18), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 3), (0, 4), (0, 8), (0, 9), (0, 12), (0, 13), (1, 9), (1, 13), (2, 8), (2, 12), (2, 13), (3, 7), (3, 9), (3, 13), (4, 5), (4, 6), (4, 10), (4, 11), (5, 6), (5, 11), (6, 8), (6, 10), (7, 8), (7, 11), (9, 13), (10, 11), (10, 12), (11, 12), (12, 13), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 1), (0, 3), (0, 9), (0, 10), (0, 12), (1, 3), (1, 7), (1, 8), (1, 10), (2, 3), (2, 5), (2, 6), (2, 9), (2, 10), (3, 6), (3, 9), (3, 10), (3, 11), (3, 12), (4, 6), (4, 9), (5, 6), (5, 7), (5, 8), (5, 12), (6, 12), (8, 12), (9, 11), (10, 11), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 1), (0, 3), (0, 5), (0, 6), (0, 10), (1, 3), (1, 5), (1, 8), (1, 9), (1, 10), (2, 3), (2, 6), (2, 8), (3, 6), (3, 7), (3, 10), (4, 5), (4, 6), (4, 7), (5, 8), (5, 9), (7, 8), (7, 10), (8, 10), (9, 10), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 13), (1, 5), (1, 8), (1, 12), (2, 9), (2, 14), (2, 16), (3, 11), (3, 15), (4, 9), (4, 13), (4, 17), (5, 6), (5, 7), (5, 15), (6, 9), (7, 11), (7, 13), (8, 13), (10, 15), (11, 14), (11, 17), (12, 13), (14, 16), (14, 17), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 4), (1, 3), (1, 9), (2, 9), (3, 7), (3, 8), (3, 9), (4, 5), (4, 7), (5, 6), (6, 7), (6, 9), (7, 8), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (1, 2), (1, 5), (1, 6), (1, 12), (2, 3), (2, 10), (3, 6), (3, 7), (3, 9), (3, 11), (3, 13), (4, 8), (4, 9), (4, 12), (4, 13), (5, 7), (5, 8), (5, 13), (6, 13), (7, 8), (7, 9), (7, 10), (7, 13), (9, 10), (9, 13), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 1), (0, 2), (0, 4), (0, 6), (0, 8), (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 9), (2, 10), (2, 12), (3, 5), (3, 6), (4, 7), (4, 12), (5, 6), (5, 8), (5, 10), (6, 10), (6, 12), (6, 13), (6, 14), (7, 12), (8, 9), (8, 10), (8, 11), (9, 12), (10, 13), (11, 12), (12, 14), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 5), (1, 3), (1, 5), (1, 6), (2, 14), (2, 15), (3, 5), (4, 7), (4, 8), (4, 12), (5, 6), (5, 12), (6, 7), (6, 13), (8, 9), (8, 14), (9, 12), (9, 16), (10, 14), (12, 14), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 1), (0, 2), (0, 5), (0, 6), (1, 4), (1, 5), (1, 7), (2, 3), (2, 6), (3, 4), (3, 8), (4, 7), (4, 9), (5, 6), (5, 7), (5, 8), (5, 9), (6, 7), (6, 8), (7, 8), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
1number_connected_components
| 0directed
| Given an undirected graph with edges (0, 10), (1, 2), (1, 7), (2, 4), (4, 10), (4, 11), (5, 8), (6, 8), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "directed", "num_workers": 1} | "5" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (1, 10), (2, 7), (3, 6), (3, 7), (4, 5), (4, 9), (5, 9), (6, 9), (8, 9), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "3" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 4), (1, 3), (1, 8), (2, 4), (2, 6), (2, 7), (2, 8), (3, 6), (3, 7), (3, 9), (5, 10), (8, 10), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 4), (0, 6), (0, 7), (0, 9), (0, 14), (1, 3), (1, 5), (1, 9), (1, 10), (1, 11), (1, 13), (2, 5), (2, 8), (2, 13), (3, 6), (3, 13), (4, 8), (4, 9), (4, 13), (4, 15), (4, 16), (5, 7), (5, 11), (5, 12), (6, 7), (7, 12), (7, 13), (9, 12), (9, 14), (11, 15), (12, 15), (15, 16), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 2), (0, 3), (0, 7), (0, 9), (0, 11), (1, 4), (1, 6), (1, 10), (1, 11), (2, 3), (2, 6), (2, 7), (2, 9), (2, 10), (3, 5), (3, 7), (3, 9), (3, 12), (3, 13), (4, 7), (4, 9), (4, 11), (4, 12), (5, 8), (5, 9), (5, 12), (5, 13), (6, 7), (6, 8), (6, 10), (6, 11), (7, 8), (7, 9), (7, 10), (7, 11), (8, 10), (9, 10), (9, 13), (10, 11), (10, 12), (10, 13), (11, 12), (11, 13), (12, 13), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 11), (0, 12), (1, 2), (1, 5), (1, 6), (1, 9), (1, 12), (2, 4), (2, 8), (2, 11), (3, 4), (4, 9), (4, 11), (5, 7), (6, 10), (7, 10), (8, 9), (8, 10), (8, 11), (10, 12), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 4), (0, 5), (0, 7), (1, 5), (1, 6), (2, 5), (2, 8), (2, 9), (3, 4), (3, 5), (4, 6), (6, 8), (7, 9), (7, 10), (9, 10), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 3), (0, 10), (0, 11), (1, 2), (1, 4), (1, 8), (1, 9), (1, 10), (1, 11), (2, 4), (2, 6), (2, 10), (2, 13), (3, 5), (3, 6), (3, 11), (3, 12), (4, 7), (4, 8), (4, 9), (5, 6), (5, 7), (5, 8), (5, 11), (5, 13), (6, 9), (6, 11), (6, 12), (7, 8), (7, 9), (8, 11), (8, 12), (8, 13), (9, 10), (10, 11), (11, 12), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 2), (0, 5), (0, 7), (1, 3), (1, 5), (2, 3), (2, 6), (4, 7), (5, 6), (5, 7), (5, 8), (5, 10), (7, 9), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 4), (0, 8), (0, 11), (1, 2), (1, 8), (1, 9), (1, 10), (1, 15), (2, 3), (2, 4), (2, 5), (2, 8), (2, 13), (2, 14), (3, 6), (3, 7), (3, 8), (3, 12), (3, 13), (4, 5), (4, 7), (5, 7), (5, 9), (5, 11), (5, 13), (5, 15), (6, 8), (6, 12), (6, 15), (7, 11), (7, 15), (8, 12), (8, 14), (8, 15), (9, 10), (10, 12), (10, 13), (11, 14), (11, 15), (12, 13), (12, 14), (12, 15), (13, 15), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 2), (0, 9), (1, 2), (1, 3), (1, 5), (1, 6), (1, 8), (1, 10), (2, 3), (2, 7), (2, 8), (2, 9), (3, 8), (3, 10), (4, 5), (4, 6), (4, 8), (4, 9), (4, 10), (5, 8), (5, 9), (6, 8), (7, 9), (7, 10), (8, 9), (9, 10), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 4), (1, 2), (1, 10), (2, 4), (2, 5), (2, 8), (2, 12), (4, 11), (4, 12), (5, 7), (5, 9), (6, 8), (7, 12), (9, 11), (10, 11), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "2" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (4, 9), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "12" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 3), (0, 4), (0, 7), (0, 8), (0, 9), (0, 10), (1, 3), (1, 9), (1, 10), (1, 11), (2, 9), (2, 11), (3, 5), (3, 12), (4, 5), (4, 10), (5, 12), (6, 9), (7, 8), (8, 12), (9, 10), (10, 13), (12, 13), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 5), (0, 10), (1, 2), (1, 3), (1, 8), (1, 10), (2, 6), (2, 8), (2, 9), (2, 10), (3, 5), (3, 9), (4, 6), (4, 7), (4, 9), (5, 7), (6, 7), (6, 9), (7, 9), (7, 10), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 2), (0, 3), (0, 5), (0, 12), (1, 4), (1, 5), (1, 10), (2, 5), (2, 6), (2, 8), (2, 9), (2, 11), (3, 6), (3, 7), (3, 12), (4, 6), (4, 9), (4, 10), (4, 11), (4, 12), (5, 8), (5, 9), (5, 10), (6, 7), (6, 9), (6, 10), (7, 8), (7, 9), (7, 11), (8, 11), (8, 12), (9, 10), (10, 12), (11, 12), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 2), (0, 3), (0, 5), (0, 6), (0, 8), (1, 2), (1, 3), (1, 4), (1, 5), (2, 5), (2, 9), (3, 8), (4, 6), (4, 7), (4, 9), (5, 7), (5, 9), (6, 7), (7, 9), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 5), (0, 7), (0, 8), (0, 12), (0, 14), (1, 3), (1, 4), (1, 6), (1, 9), (1, 10), (1, 12), (1, 13), (2, 5), (2, 6), (2, 8), (2, 9), (2, 11), (2, 13), (2, 14), (3, 4), (3, 5), (3, 11), (3, 13), (4, 7), (4, 9), (4, 11), (4, 13), (4, 14), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (5, 13), (6, 7), (6, 9), (6, 11), (6, 14), (7, 9), (7, 10), (7, 13), (7, 14), (8, 11), (8, 13), (9, 11), (9, 13), (9, 14), (10, 11), (10, 12), (10, 13), (11, 12), (12, 13), (12, 14), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 5), (0, 8), (0, 9), (0, 10), (0, 11), (0, 13), (1, 10), (1, 12), (1, 13), (2, 9), (2, 10), (2, 11), (2, 12), (3, 7), (3, 9), (3, 13), (4, 11), (4, 13), (5, 6), (5, 7), (6, 9), (6, 10), (6, 13), (7, 10), (7, 11), (7, 13), (8, 9), (8, 13), (9, 10), (9, 12), (9, 13), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 2), (0, 6), (0, 9), (0, 11), (1, 2), (1, 3), (1, 6), (1, 7), (1, 9), (2, 7), (2, 12), (3, 4), (3, 6), (3, 11), (4, 6), (4, 7), (4, 10), (4, 11), (4, 12), (5, 6), (5, 7), (5, 8), (6, 10), (6, 12), (7, 8), (8, 10), (9, 10), (9, 13), (11, 13), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 3), (0, 5), (0, 11), (0, 12), (1, 2), (1, 4), (1, 5), (1, 10), (1, 14), (2, 5), (2, 9), (2, 11), (2, 13), (2, 14), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 10), (3, 11), (3, 12), (3, 14), (4, 5), (4, 8), (4, 10), (4, 13), (5, 6), (5, 7), (5, 12), (6, 12), (6, 14), (7, 9), (7, 12), (7, 14), (8, 12), (8, 13), (10, 11), (10, 14), (11, 13), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 5), (0, 8), (0, 11), (0, 15), (0, 16), (0, 17), (0, 18), (0, 19), (1, 2), (1, 3), (1, 5), (1, 6), (1, 8), (1, 10), (1, 14), (1, 15), (2, 3), (2, 11), (2, 12), (2, 13), (3, 5), (3, 6), (3, 7), (3, 10), (3, 12), (3, 13), (3, 15), (3, 16), (4, 7), (4, 10), (4, 15), (4, 16), (5, 6), (5, 7), (5, 12), (5, 13), (5, 15), (5, 17), (5, 18), (5, 19), (6, 7), (6, 10), (6, 11), (6, 12), (6, 13), (6, 14), (6, 17), (6, 18), (6, 19), (7, 10), (7, 13), (7, 15), (7, 19), (8, 10), (8, 12), (8, 13), (8, 15), (8, 18), (8, 19), (9, 10), (9, 16), (9, 18), (10, 12), (10, 13), (10, 17), (10, 18), (11, 12), (11, 14), (11, 18), (11, 19), (12, 13), (12, 15), (12, 16), (12, 17), (12, 18), (13, 14), (13, 16), (13, 18), (13, 19), (14, 16), (14, 17), (14, 19), (15, 16), (15, 17), (15, 18), (15, 19), (16, 17), (17, 18), (17, 19), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 4), (0, 5), (0, 13), (0, 14), (1, 4), (1, 5), (1, 10), (1, 12), (1, 13), (1, 14), (2, 3), (2, 4), (2, 6), (2, 7), (2, 9), (2, 13), (3, 4), (3, 5), (3, 6), (3, 8), (3, 10), (3, 11), (3, 14), (4, 8), (4, 10), (4, 11), (4, 13), (4, 14), (5, 6), (5, 7), (5, 8), (5, 9), (6, 8), (6, 10), (6, 11), (6, 12), (6, 13), (7, 8), (7, 11), (7, 12), (8, 10), (9, 11), (9, 12), (9, 13), (9, 14), (10, 11), (10, 14), (11, 12), (11, 14), (12, 13), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 7), (2, 4), (3, 7), (4, 5), (5, 7), (6, 7), (6, 8), (8, 9), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "2" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (1, 9), (2, 4), (2, 5), (2, 6), (2, 11), (3, 4), (3, 5), (5, 7), (5, 11), (6, 11), (7, 9), (8, 10), (9, 10), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "2" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 3), (0, 4), (0, 5), (0, 14), (0, 16), (1, 4), (1, 5), (1, 11), (2, 5), (2, 6), (2, 7), (2, 8), (2, 15), (2, 17), (3, 6), (3, 7), (3, 17), (4, 7), (4, 9), (4, 17), (5, 6), (5, 8), (5, 11), (5, 12), (5, 15), (5, 17), (6, 11), (6, 13), (6, 17), (7, 8), (8, 9), (8, 13), (10, 11), (10, 14), (11, 13), (11, 14), (13, 14), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 2), (0, 3), (0, 5), (0, 7), (0, 8), (0, 13), (0, 16), (0, 18), (1, 2), (1, 4), (1, 5), (1, 6), (1, 8), (1, 12), (1, 13), (1, 15), (1, 16), (1, 17), (2, 3), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 12), (2, 13), (2, 14), (2, 16), (2, 17), (2, 18), (3, 9), (3, 10), (3, 11), (3, 12), (3, 15), (3, 17), (3, 18), (4, 7), (4, 8), (4, 12), (4, 15), (4, 17), (5, 10), (5, 11), (5, 12), (5, 14), (5, 16), (6, 8), (6, 11), (6, 14), (7, 10), (7, 11), (7, 12), (7, 13), (7, 15), (7, 17), (7, 18), (8, 10), (8, 16), (8, 18), (9, 11), (9, 12), (9, 13), (9, 14), (9, 15), (9, 16), (9, 17), (10, 11), (10, 14), (10, 15), (10, 18), (11, 12), (11, 13), (11, 15), (11, 16), (12, 14), (12, 16), (12, 17), (12, 18), (13, 15), (13, 17), (14, 15), (14, 16), (15, 17), (16, 18), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 4), (0, 8), (0, 9), (0, 10), (0, 12), (1, 6), (1, 7), (1, 8), (1, 12), (1, 14), (2, 3), (2, 6), (2, 10), (2, 11), (3, 4), (3, 5), (3, 7), (3, 8), (3, 11), (3, 13), (4, 6), (4, 7), (4, 9), (4, 10), (4, 13), (4, 14), (5, 7), (5, 8), (5, 9), (5, 14), (6, 8), (6, 11), (6, 12), (6, 14), (7, 8), (7, 9), (7, 10), (7, 11), (7, 13), (8, 9), (8, 11), (8, 14), (9, 10), (9, 12), (9, 13), (10, 12), (11, 14), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 6), (0, 7), (0, 10), (1, 2), (1, 4), (1, 5), (1, 7), (1, 8), (1, 10), (2, 9), (3, 6), (4, 6), (4, 8), (4, 9), (4, 10), (5, 7), (5, 8), (5, 10), (6, 7), (6, 8), (6, 9), (6, 10), (7, 9), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 5), (0, 6), (0, 8), (1, 2), (2, 3), (2, 5), (3, 6), (5, 6), (6, 7), (6, 8), (8, 9), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "2" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 5), (0, 6), (0, 9), (0, 10), (1, 10), (2, 4), (3, 10), (4, 10), (5, 7), (6, 9), (8, 10), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 5), (1, 3), (1, 5), (1, 17), (3, 4), (3, 17), (4, 15), (5, 7), (7, 10), (8, 9), (8, 13), (9, 15), (10, 13), (12, 15), (13, 15), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "6" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 5), (0, 8), (0, 12), (0, 14), (1, 2), (1, 9), (2, 3), (2, 7), (2, 13), (2, 14), (3, 12), (4, 8), (4, 10), (4, 12), (4, 14), (4, 15), (4, 17), (5, 6), (5, 11), (5, 14), (5, 16), (6, 9), (6, 12), (6, 14), (6, 16), (6, 17), (7, 8), (7, 12), (8, 9), (8, 13), (8, 15), (8, 16), (9, 16), (9, 17), (10, 14), (11, 17), (12, 15), (13, 17), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 2), (0, 4), (0, 8), (0, 11), (0, 13), (0, 15), (1, 5), (1, 8), (1, 10), (1, 13), (1, 15), (2, 5), (2, 8), (2, 9), (2, 11), (2, 13), (2, 14), (2, 15), (3, 4), (3, 7), (3, 9), (3, 10), (3, 11), (3, 14), (4, 7), (4, 9), (4, 13), (4, 14), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (5, 12), (5, 15), (6, 9), (6, 10), (6, 12), (6, 14), (6, 15), (7, 8), (7, 10), (8, 10), (8, 11), (8, 13), (9, 14), (9, 15), (10, 11), (10, 12), (10, 14), (10, 15), (11, 15), (12, 13), (12, 14), (12, 15), (13, 14), (13, 15), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 3), (1, 5), (1, 8), (2, 4), (2, 8), (2, 10), (3, 5), (3, 8), (4, 5), (4, 10), (5, 6), (5, 9), (6, 7), (7, 8), (7, 9), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 2), (0, 3), (0, 11), (0, 12), (1, 2), (1, 6), (1, 7), (1, 8), (1, 11), (1, 12), (1, 13), (1, 14), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 9), (2, 10), (2, 12), (2, 15), (3, 5), (4, 8), (4, 9), (4, 16), (4, 17), (5, 6), (5, 9), (5, 10), (5, 12), (5, 13), (5, 16), (6, 7), (6, 9), (6, 10), (6, 12), (6, 13), (6, 15), (6, 16), (6, 17), (7, 8), (7, 11), (7, 12), (7, 14), (7, 16), (8, 10), (9, 11), (9, 12), (9, 14), (9, 16), (9, 17), (10, 11), (11, 14), (11, 15), (11, 16), (11, 17), (12, 14), (12, 15), (12, 16), (12, 17), (14, 16), (14, 17), (15, 16), (15, 17), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 2), (0, 4), (1, 3), (1, 4), (1, 6), (2, 8), (3, 6), (3, 9), (4, 7), (5, 7), (6, 10), (7, 10), (9, 10), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 12), (0, 14), (1, 2), (1, 3), (1, 4), (1, 6), (1, 7), (1, 13), (1, 14), (2, 7), (2, 10), (2, 11), (2, 12), (2, 14), (3, 6), (3, 10), (3, 12), (4, 6), (4, 14), (5, 8), (5, 11), (6, 7), (6, 10), (6, 12), (7, 8), (7, 12), (9, 11), (10, 13), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 5), (0, 7), (0, 9), (0, 12), (1, 3), (1, 4), (1, 5), (1, 6), (1, 13), (2, 5), (2, 6), (2, 12), (3, 4), (3, 6), (3, 12), (4, 5), (4, 8), (4, 11), (4, 13), (5, 10), (5, 11), (5, 12), (5, 13), (6, 9), (6, 11), (6, 13), (7, 11), (7, 12), (8, 9), (8, 11), (8, 13), (9, 13), (10, 12), (11, 12), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 7), (0, 9), (0, 11), (0, 13), (0, 16), (0, 19), (1, 2), (1, 3), (1, 4), (1, 5), (1, 7), (1, 8), (1, 9), (1, 11), (1, 14), (1, 16), (2, 3), (2, 9), (2, 10), (2, 12), (2, 14), (2, 16), (2, 17), (2, 18), (3, 6), (3, 12), (3, 14), (3, 18), (4, 5), (4, 7), (4, 8), (4, 10), (4, 11), (4, 12), (4, 14), (4, 15), (4, 16), (4, 17), (4, 19), (5, 6), (5, 8), (5, 11), (5, 14), (5, 15), (5, 19), (6, 8), (6, 9), (6, 10), (6, 11), (6, 14), (6, 15), (6, 17), (6, 18), (7, 9), (7, 12), (7, 14), (7, 17), (8, 9), (8, 10), (8, 13), (8, 14), (8, 16), (8, 17), (9, 15), (9, 16), (9, 18), (10, 12), (10, 14), (10, 15), (10, 16), (10, 17), (11, 14), (12, 15), (12, 16), (12, 18), (13, 15), (13, 17), (13, 18), (14, 16), (14, 17), (14, 19), (15, 16), (15, 19), (16, 18), (16, 19), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
1number_connected_components
| 1undirected
| Given an undirected graph with edges (0, 1), (0, 2), (0, 5), (0, 6), (0, 9), (0, 13), (1, 2), (1, 3), (1, 6), (1, 10), (1, 11), (2, 4), (2, 10), (2, 11), (2, 12), (3, 4), (3, 6), (3, 7), (3, 9), (3, 10), (3, 12), (4, 9), (4, 12), (4, 13), (5, 11), (5, 12), (6, 9), (7, 8), (7, 10), (7, 11), (7, 13), (8, 10), (8, 13), (9, 11), (9, 13), (11, 12), what is its number of connected components, the number of connected components? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "number_connected_components", "samples": 40, "graph_type": "undirected", "num_workers": 1} | "1" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 2), (0, 3), (0, 10), (0, 13), (1, 10), (1, 14), (2, 3), (2, 6), (2, 9), (2, 10), (3, 12), (4, 5), (4, 7), (4, 9), (4, 10), (4, 14), (8, 10), (8, 11), (8, 13), (8, 14), (9, 12), (10, 12), (10, 14), (11, 12), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 5), (0, 7), (0, 8), (0, 9), (0, 10), (0, 11), (0, 13), (0, 17), (0, 18), (1, 2), (1, 4), (1, 7), (1, 8), (1, 16), (2, 6), (2, 8), (2, 11), (2, 14), (2, 18), (3, 4), (3, 8), (3, 9), (3, 13), (3, 17), (4, 7), (4, 8), (4, 11), (4, 15), (4, 17), (5, 6), (5, 8), (5, 9), (5, 10), (5, 11), (5, 12), (5, 15), (5, 16), (6, 8), (6, 12), (6, 13), (6, 15), (6, 19), (7, 12), (7, 14), (7, 19), (8, 11), (8, 13), (8, 14), (8, 15), (8, 16), (8, 19), (9, 11), (9, 12), (9, 14), (9, 19), (10, 11), (10, 13), (10, 18), (10, 19), (11, 17), (11, 18), (12, 13), (12, 14), (12, 17), (13, 15), (13, 18), (13, 19), (14, 18), (15, 16), (15, 17), (17, 18), (18, 19), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "4" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 9), (0, 18), (1, 6), (2, 10), (3, 16), (3, 19), (4, 6), (5, 6), (5, 9), (5, 12), (7, 11), (7, 16), (7, 19), (8, 11), (9, 15), (9, 16), (10, 18), (11, 13), (15, 18), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 4), (0, 10), (1, 2), (1, 3), (1, 12), (2, 3), (3, 9), (4, 7), (4, 9), (5, 10), (6, 10), (6, 13), (6, 14), (7, 10), (7, 12), (8, 13), (10, 11), (10, 12), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 9), (0, 10), (0, 11), (1, 2), (1, 4), (1, 5), (1, 8), (1, 9), (2, 3), (2, 6), (2, 10), (2, 11), (3, 4), (3, 5), (3, 7), (3, 8), (3, 9), (4, 5), (4, 6), (4, 8), (4, 11), (5, 6), (5, 8), (6, 9), (6, 10), (7, 8), (7, 11), (8, 10), (9, 10), (10, 11), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "3" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 2), (0, 3), (0, 6), (0, 8), (0, 10), (1, 2), (1, 3), (1, 5), (1, 7), (1, 10), (1, 11), (2, 4), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 9), (3, 11), (4, 6), (4, 8), (4, 11), (5, 6), (5, 7), (5, 10), (6, 7), (6, 9), (7, 11), (9, 10), (10, 11), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "3" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 3), (0, 4), (0, 5), (0, 8), (0, 9), (0, 10), (1, 3), (1, 5), (1, 8), (2, 3), (2, 5), (2, 6), (2, 7), (2, 8), (2, 10), (3, 5), (3, 7), (3, 9), (4, 6), (4, 8), (4, 9), (5, 9), (6, 7), (6, 9), (9, 10), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "3" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 5), (0, 9), (0, 11), (1, 4), (1, 12), (2, 3), (2, 5), (2, 8), (2, 9), (2, 12), (2, 15), (3, 4), (3, 6), (3, 7), (3, 11), (3, 14), (4, 5), (4, 6), (4, 11), (4, 16), (4, 18), (5, 11), (6, 7), (6, 9), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (7, 8), (7, 11), (7, 13), (7, 16), (7, 17), (8, 11), (8, 16), (9, 13), (9, 15), (9, 18), (10, 13), (10, 17), (11, 13), (11, 16), (11, 18), (12, 16), (13, 18), (14, 15), (14, 16), (15, 17), (16, 18), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 3), (0, 8), (0, 9), (0, 10), (0, 13), (1, 3), (1, 6), (1, 10), (1, 15), (2, 4), (2, 5), (2, 14), (3, 10), (3, 13), (4, 12), (5, 7), (5, 14), (6, 8), (6, 11), (7, 9), (7, 13), (7, 15), (8, 10), (8, 14), (9, 11), (10, 12), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 2), (0, 3), (0, 6), (0, 11), (0, 13), (0, 14), (0, 18), (1, 7), (1, 8), (1, 12), (1, 14), (1, 17), (2, 5), (2, 7), (2, 13), (2, 15), (2, 16), (2, 17), (2, 18), (3, 5), (3, 11), (3, 12), (3, 15), (3, 16), (4, 5), (4, 10), (4, 11), (4, 12), (4, 18), (5, 7), (5, 9), (5, 11), (5, 14), (5, 17), (6, 9), (6, 13), (6, 17), (7, 8), (8, 9), (8, 11), (8, 12), (8, 17), (8, 18), (9, 11), (9, 12), (11, 13), (11, 14), (11, 17), (11, 18), (12, 14), (12, 15), (13, 14), (13, 15), (13, 17), (13, 18), (14, 18), (16, 18), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 3), (0, 13), (1, 4), (1, 6), (1, 8), (1, 10), (1, 13), (2, 9), (2, 11), (2, 14), (3, 4), (3, 5), (3, 6), (3, 9), (4, 13), (6, 11), (6, 12), (8, 12), (10, 12), (11, 14), (12, 14), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 2), (0, 5), (0, 8), (0, 9), (0, 12), (1, 5), (1, 6), (1, 7), (1, 9), (2, 3), (2, 4), (2, 6), (2, 10), (2, 12), (3, 6), (3, 9), (3, 10), (3, 12), (4, 5), (4, 6), (4, 7), (4, 11), (4, 12), (5, 6), (5, 7), (5, 8), (5, 12), (6, 9), (6, 12), (7, 10), (7, 11), (7, 12), (8, 9), (8, 10), (8, 11), (8, 12), (9, 11), (11, 12), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "4" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 2), (0, 3), (0, 13), (1, 3), (1, 5), (1, 6), (1, 9), (1, 12), (2, 6), (2, 8), (2, 9), (2, 10), (2, 11), (3, 7), (3, 11), (4, 5), (4, 8), (4, 11), (5, 8), (5, 9), (6, 11), (6, 12), (6, 13), (7, 12), (8, 13), (9, 10), (9, 13), (10, 12), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 7), (0, 9), (0, 14), (0, 15), (1, 4), (1, 11), (1, 12), (1, 13), (1, 14), (2, 4), (2, 5), (2, 6), (2, 7), (2, 12), (3, 5), (3, 6), (3, 8), (3, 12), (4, 5), (4, 8), (4, 9), (4, 10), (4, 12), (4, 15), (5, 12), (6, 8), (6, 15), (7, 9), (7, 10), (7, 12), (8, 11), (8, 13), (9, 11), (9, 12), (10, 14), (10, 15), (11, 12), (11, 15), (13, 14), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "3" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 3), (0, 7), (0, 11), (0, 14), (1, 2), (1, 9), (1, 15), (2, 3), (2, 4), (2, 5), (2, 7), (2, 13), (2, 15), (2, 16), (2, 17), (3, 5), (3, 12), (3, 16), (3, 18), (4, 5), (4, 6), (4, 7), (4, 10), (4, 12), (4, 17), (5, 6), (5, 8), (5, 11), (5, 18), (6, 8), (6, 14), (6, 15), (6, 16), (7, 8), (7, 9), (7, 14), (7, 16), (7, 17), (7, 18), (8, 10), (8, 12), (8, 15), (8, 16), (8, 17), (9, 14), (9, 16), (9, 17), (10, 15), (10, 17), (11, 15), (11, 17), (11, 18), (12, 17), (13, 16), (14, 18), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 2), (0, 5), (0, 7), (0, 9), (0, 11), (0, 13), (0, 15), (0, 16), (0, 18), (1, 3), (1, 5), (1, 8), (1, 10), (1, 13), (1, 15), (1, 18), (2, 5), (2, 6), (2, 8), (2, 10), (2, 19), (3, 5), (3, 6), (3, 9), (3, 11), (3, 17), (3, 19), (4, 7), (4, 8), (4, 11), (4, 12), (4, 15), (4, 16), (5, 15), (6, 10), (6, 11), (6, 12), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (7, 8), (7, 11), (7, 13), (7, 17), (7, 18), (7, 19), (8, 11), (8, 12), (8, 14), (8, 16), (8, 18), (9, 11), (9, 17), (9, 18), (9, 19), (10, 12), (10, 16), (10, 19), (11, 16), (11, 19), (12, 17), (12, 18), (13, 14), (13, 15), (13, 18), (13, 19), (14, 15), (16, 19), (17, 18), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "4" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 4), (0, 12), (0, 13), (1, 5), (1, 7), (1, 8), (1, 9), (1, 11), (1, 13), (2, 5), (2, 8), (2, 11), (3, 7), (3, 8), (3, 10), (3, 11), (3, 12), (4, 7), (4, 8), (4, 9), (4, 12), (5, 6), (5, 8), (6, 8), (6, 9), (6, 10), (6, 11), (6, 13), (7, 9), (8, 9), (8, 12), (9, 10), (9, 13), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "3" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 2), (0, 8), (0, 9), (0, 10), (0, 14), (0, 15), (1, 3), (1, 4), (1, 7), (1, 8), (1, 13), (1, 15), (2, 3), (2, 4), (2, 6), (2, 7), (2, 9), (3, 4), (3, 10), (3, 15), (4, 6), (4, 7), (4, 8), (4, 9), (4, 11), (4, 15), (4, 16), (4, 17), (5, 12), (5, 13), (5, 17), (6, 7), (6, 9), (6, 12), (6, 18), (7, 8), (7, 10), (7, 12), (7, 16), (7, 17), (7, 18), (8, 10), (8, 12), (8, 13), (8, 14), (8, 15), (8, 18), (9, 12), (9, 15), (10, 11), (10, 15), (10, 16), (10, 17), (11, 12), (11, 13), (11, 15), (11, 17), (12, 15), (12, 17), (13, 16), (14, 18), (15, 16), (17, 18), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "3" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 2), (0, 5), (0, 8), (0, 14), (1, 2), (1, 8), (1, 10), (1, 11), (1, 16), (2, 3), (2, 4), (2, 5), (2, 7), (3, 5), (3, 6), (3, 9), (3, 13), (3, 16), (4, 13), (5, 6), (5, 9), (5, 13), (8, 9), (8, 12), (8, 16), (9, 13), (11, 12), (12, 16), (14, 16), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 2), (0, 8), (1, 3), (1, 7), (1, 8), (1, 10), (2, 5), (3, 7), (4, 10), (5, 10), (8, 9), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 2), (0, 4), (0, 8), (0, 10), (0, 11), (0, 15), (1, 4), (1, 5), (1, 7), (1, 11), (1, 12), (1, 13), (1, 14), (1, 16), (2, 4), (2, 5), (2, 6), (2, 7), (2, 10), (2, 12), (2, 13), (2, 19), (3, 4), (3, 13), (3, 16), (3, 18), (4, 6), (4, 10), (4, 11), (4, 13), (4, 16), (4, 17), (5, 6), (5, 7), (5, 8), (5, 10), (5, 15), (5, 17), (6, 7), (6, 14), (6, 16), (6, 18), (7, 13), (7, 14), (7, 15), (7, 17), (8, 11), (8, 16), (8, 17), (8, 18), (9, 13), (9, 15), (9, 16), (9, 18), (10, 12), (10, 16), (10, 17), (10, 18), (10, 19), (11, 15), (11, 17), (11, 18), (11, 19), (12, 13), (12, 14), (12, 16), (12, 18), (12, 19), (13, 14), (13, 15), (13, 16), (13, 17), (14, 17), (14, 18), (14, 19), (15, 18), (15, 19), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "4" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 5), (0, 6), (0, 9), (0, 11), (1, 8), (1, 13), (2, 3), (2, 9), (2, 12), (4, 6), (6, 12), (7, 11), (7, 12), (8, 9), (8, 11), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 2), (0, 3), (1, 4), (2, 3), (2, 7), (4, 5), (4, 10), (5, 10), (6, 7), (6, 8), (6, 11), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 2), (0, 3), (0, 7), (0, 11), (1, 3), (1, 4), (2, 6), (2, 7), (3, 6), (3, 7), (3, 16), (4, 6), (4, 7), (4, 9), (4, 10), (4, 11), (4, 12), (4, 14), (5, 10), (5, 14), (6, 7), (6, 10), (6, 12), (7, 9), (7, 11), (7, 12), (7, 16), (8, 11), (8, 12), (8, 14), (8, 15), (9, 11), (9, 12), (9, 13), (9, 15), (10, 15), (10, 16), (13, 15), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 2), (0, 7), (2, 6), (3, 4), (6, 9), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 9), (1, 5), (2, 3), (2, 8), (2, 9), (3, 4), (3, 9), (4, 9), (6, 8), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 9), (1, 5), (1, 9), (2, 6), (2, 7), (3, 11), (4, 8), (8, 9), (8, 10), (9, 10), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 2), (0, 3), (0, 13), (0, 14), (0, 15), (1, 3), (1, 6), (1, 7), (1, 8), (1, 10), (1, 14), (2, 4), (2, 5), (2, 7), (2, 9), (2, 14), (2, 15), (3, 4), (3, 6), (3, 7), (3, 8), (3, 11), (4, 5), (4, 6), (4, 7), (4, 8), (4, 12), (4, 15), (5, 7), (5, 9), (5, 10), (5, 13), (5, 14), (6, 7), (6, 10), (6, 11), (6, 15), (7, 8), (7, 11), (7, 14), (8, 9), (8, 10), (8, 14), (9, 11), (9, 12), (10, 11), (10, 12), (11, 13), (11, 14), (11, 15), (12, 14), (12, 15), (13, 15), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "4" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 4), (0, 5), (0, 6), (0, 9), (1, 2), (1, 8), (2, 4), (2, 7), (2, 9), (3, 4), (4, 5), (4, 10), (5, 9), (6, 9), (6, 10), (8, 10), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 4), (0, 6), (0, 8), (1, 2), (1, 5), (1, 11), (2, 5), (2, 7), (2, 11), (2, 12), (3, 4), (3, 5), (3, 7), (3, 8), (3, 11), (4, 8), (4, 9), (5, 9), (5, 10), (6, 10), (7, 9), (8, 13), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 7), (0, 11), (0, 15), (1, 8), (2, 4), (2, 7), (2, 13), (3, 6), (3, 7), (3, 11), (4, 10), (4, 13), (5, 6), (5, 8), (5, 11), (7, 15), (8, 15), (9, 13), (12, 14), (14, 15), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 3), (0, 9), (0, 12), (1, 3), (1, 7), (1, 11), (1, 12), (1, 13), (2, 4), (2, 6), (2, 7), (2, 8), (2, 11), (3, 5), (3, 6), (3, 7), (3, 10), (3, 12), (4, 6), (4, 8), (4, 9), (4, 11), (4, 13), (5, 6), (5, 10), (5, 12), (5, 13), (6, 8), (6, 10), (7, 13), (9, 10), (9, 11), (9, 13), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "3" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 7), (0, 8), (0, 13), (1, 2), (1, 6), (1, 8), (1, 10), (1, 12), (1, 14), (1, 15), (2, 11), (2, 12), (2, 14), (3, 9), (3, 12), (3, 15), (4, 5), (4, 7), (4, 12), (5, 10), (6, 8), (6, 9), (6, 13), (6, 14), (6, 15), (7, 9), (7, 10), (7, 11), (9, 10), (9, 12), (9, 14), (10, 11), (10, 13), (10, 14), (11, 12), (11, 13), (11, 14), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 4), (0, 7), (0, 10), (1, 2), (1, 3), (1, 6), (1, 7), (1, 8), (1, 9), (2, 5), (2, 6), (2, 7), (2, 8), (2, 10), (3, 7), (3, 10), (4, 7), (4, 8), (5, 7), (5, 8), (5, 9), (6, 9), (6, 10), (7, 8), (7, 9), (9, 10), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "3" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 8), (0, 9), (1, 2), (1, 4), (1, 5), (1, 7), (1, 8), (1, 9), (2, 4), (2, 8), (2, 9), (3, 4), (5, 6), (5, 8), (7, 8), (8, 9), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 9), (0, 10), (0, 15), (1, 6), (2, 6), (2, 9), (2, 10), (2, 15), (3, 13), (3, 16), (4, 5), (5, 7), (5, 8), (5, 9), (6, 10), (6, 15), (8, 10), (8, 12), (8, 13), (8, 15), (9, 11), (9, 13), (9, 16), (10, 13), (11, 14), (11, 16), (12, 15), (12, 16), (13, 16), (14, 15), (14, 16), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "1" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 2), (0, 4), (0, 5), (0, 6), (1, 3), (1, 4), (1, 5), (1, 8), (2, 3), (2, 5), (2, 6), (2, 9), (3, 4), (3, 6), (3, 7), (3, 9), (4, 5), (4, 9), (5, 6), (5, 7), (6, 8), (6, 9), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "2" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 4), (0, 5), (0, 8), (0, 9), (0, 11), (1, 2), (1, 3), (1, 5), (1, 6), (1, 8), (1, 11), (2, 3), (2, 6), (2, 7), (2, 10), (2, 11), (3, 4), (3, 8), (3, 9), (3, 10), (3, 11), (4, 7), (4, 10), (5, 9), (5, 10), (6, 10), (6, 11), (7, 10), (8, 9), (8, 10), (10, 11), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "3" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (2, 3), (3, 4), (4, 11), (6, 7), (10, 11), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "0" |
2node_connectivity
| 0directed
| Given an undirected graph with edges (0, 1), (0, 3), (0, 5), (0, 7), (0, 9), (0, 11), (0, 12), (0, 13), (0, 14), (0, 17), (0, 18), (1, 4), (1, 6), (1, 9), (1, 10), (1, 11), (1, 13), (1, 15), (1, 17), (2, 5), (2, 7), (2, 8), (2, 13), (2, 15), (2, 17), (2, 18), (2, 19), (3, 5), (3, 6), (3, 8), (3, 10), (3, 12), (3, 13), (3, 15), (3, 16), (3, 17), (4, 12), (4, 14), (4, 15), (4, 16), (4, 18), (4, 19), (5, 7), (5, 8), (5, 11), (5, 12), (5, 15), (5, 16), (5, 18), (6, 9), (6, 12), (6, 14), (6, 19), (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 14), (7, 17), (8, 11), (8, 13), (8, 14), (8, 15), (8, 17), (8, 18), (8, 19), (9, 10), (9, 16), (9, 18), (9, 19), (10, 13), (10, 14), (10, 15), (10, 16), (10, 17), (10, 18), (11, 15), (11, 16), (12, 13), (12, 14), (12, 15), (12, 17), (12, 18), (13, 14), (13, 17), (14, 17), (14, 18), (14, 19), (15, 17), (15, 19), (16, 18), (17, 19), (18, 19), what is its NodeConnectivity, Node connectivity is equal to the minimum number of nodes that must be removed to disconnect G or render it trivial.? Return the answer in \boxed{} format. If the answer is a floating point number, round it to 2 decimal places. If the graph is not connected and the property is undefined, return 'None'. | {"task": "node_connectivity", "samples": 40, "graph_type": "directed", "num_workers": 1} | "6" |