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| Models | Cycle | Connect | Bipartite | Topology | Shortest | Triangle | Flow | Hamilton | Subgraph | Average |
|---|---|---|---|---|---|---|---|---|---|---|
| In-Context Learning | ||||||||||
| GPT-4 (zero-shot) | 38.75 | 17.00 | 65.25 | 5.00 | 9.25 | 5.75 | 3.25 | 59.25 | 45.50 | 27.67 |
| GhatGPT (2-shot) | 51.25 | 43.75 | 70.75 | 4.50 | 3.50 | 17.25 | 8.50 | 54.25 | 43.00 | 32.97 |
| GPT-4 (2-shot) | 52.50 | 62.75 | 74.25 | 25.25 | 18.25 | 31.00 | 7.75 | {75.75} | 46.75 | 43.81 |
| Mistral-7B | ||||||||||
| Naive SFT | 73.75 | 83.50 | 78.50 | 1.00 | 23.00 | 47.00 | 28.75 | 31.75 | 41.25 | 46.56 |
| GraphWiz | 92.00 | 89.50 | 72.00 | 19.00 | 31.25 | 38.75 | 29.25 | 26.50 | 85.50 | 53.75 |
| GraphWiz-DPO | 85.50 | 79.50 | 85.50 | 85.25 | 12.50 | 29.00 | 35.50 | 62.75 | 48.50 | 58.22 |
| LLaMA 2-7B | ||||||||||
| Naive SFT | 73.75 | 83.50 | 41.25 | 4.00 | 9.50 | 30.00 | 16.50 | 69.00 | 75.45 | 44.81 |
| GraphWiz | 91.50 | 87.00 | 74.00 | 18.00 | 28.00 | 38.25 | 24.50 | 52.25 | 82.25 | 55.08 |
| GraphWiz-DPO | 89.00 | 82.50 | 84.75 | 46.75 | 24.00 | 52.75 | 43.50 | 81.50 | 77.25 | 65.00 |
| LLaMA 2-13B | ||||||||||
| Naive SFT | 73.75 | 83.75 | 59.00 | 0.50 | 11.75 | 34.75 | 24.25 | 59.75 | 54.75 | 44.69 |
| GraphWiz | 94.75 | 87.00 | 78.00 | 28.00 | 27.75 | 36.00 | 24.50 | 59.00 | 81.50 | 57.39 |
| GraphWiz-DPO | 87.50 | 88.50 | 88.25 | 72.75 | 22.00 | 48.75 | 43.75 | 46.50 | 77.00 | 63.89 |
G-Q: Determine whether or not there is a cycle in an undirected graph. In an undirected graph..,the
nodes are numbered from 0 to 88, and the edges are: (0, 73) (0, 51) (0, 10) (0, 63) (0, 28) (1, 62) (1, 57) (1, 84) (1, 61) (1, 5)
(1, 24) (2, 84) (2, 3) (2, 66) (2, 68) (2, 17) (2, 35) (2, 34) (2, 15) (3, 39) (3, 52) (3, 16) (3, 15) (3, 8) (4, 69) (4, 85)
(4, 36) (4, 72) (5, 44) (6, 77) (6, 7) (7, 85) (8, 64) (8, 23) (8, 28) (9, 34) (9, 31) (9, 61) (9, 28) (10, 26) (11, 37) (11, 39)
(11, 19) (11, 64) (13, 73) (13, 61) (13, 80) (13, 85) (14, 86) (14, 59) (14, 32) (14, 58) (14, 85) (14, 66) (15, 43) (15, 48) (15, 73)
(15, 19) (15, 47) (15, 68) (16, 46) (16, 60) (16, 84) (17, 44) (17, 72) (17, 36) (17, 37) (17, 61) (18, 20) (18, 24) (18, 22) (18, 41)
(19, 45) (19, 83) (20, 25) (20, 29) (21, 38) (21, 64) (21, 24) (21, 22) (21, 34) (22, 23) (23, 34) (23, 30) (23, 83) (24, 47) (24, 50)
(25, 59) (25, 42) (25, 70) (25, 72) (26, 45) (26, 30) (26, 87) (26, 80) (26, 50) (27, 77) (27, 58) (27, 60) (27, 29) (28, 36) (28, 59)
(28, 88) (29, 31) (29, 33) (29, 56) (29, 55) (29, 78) (29, 73) (29, 82) (30, 34) (31, 58) (31, 70) (32, 78) (33, 73) (33, 68) (34, 48)
(34, 88) (34, 51) (34, 66) (34, 54) (35, 43) (35, 56) (36, 44) (36, 39) (37, 57) (37, 71) (38, 47) (38, 58) (38, 88) (39, 74) (39, 48)
(39, 45) (39, 42) (40, 60) (40, 59) (40, 71) (40, 76) (41, 79) (42, 60) (42, 62) (42, 72) (43, 57) (44, 47) (44, 74) (44, 75) (44, 82)
(44, 70) (45, 68) (45, 67) (45, 71) (46, 84) (47, 56) (48, 75) (49, 71) (49, 58) (50, 76) (51, 55) (51, 87) (51, 79) (52, 78) (56, 69)
(56, 83) (56, 79) (57, 76) (57, 70) (57, 72) (57, 78) (59, 70) (60, 80) (60, 76) (60, 77) (60, 75) (61, 74) (61, 77) (62, 84) (62, 66)
(66, 69) (68, 88) (70, 88) (70, 76) (71, 81) (71, 72) (71, 86) (72, 75) (73, 82) (73, 83) (74, 85). Is there a cycle in this graph?
GraphWiz:
There are many possible ways to find a cycle in this graph, but one example is: Starting from node 0, we can go to node 73 (via edge 0-73), then to node 82 (via edge 73-82),
then to node 44 (via edge 82-44), then to node 17 (via edge 44-17), then to node 36 (via edge 17-36), then to node 28 (via edge 36-28),
and back to node 0 (via edge 28-0). This forms a cycle [0-73-82-44-17-36-28-0] without revisiting any edge. So, there is a cycle in this graph.