# Find all cycles in an undirected graph

For **directed** graphs, we have a built-in command `all_simple_cycles`

to search for specific length cycles or all cycles. However, it is indeed strange that there is no readily available command for undirected graphs. Although, we can convert an undirected graph into a directed graph by assigning two directions to each edge. For example:

```
g = graphs.CompleteGraph(4).to_directed();
all_cycles=g.all_simple_cycles()
print(all_cycles)
```

`[[0, 1, 0], [0, 2, 0], [0, 3, 0], [1, 2, 1], [1, 3, 1], [2, 3, 2], [0, 1, 2, 0], [0, 1, 3, 0], [0, 2, 1, 0], [0, 2, 3, 0], [0, 3, 1, 0], [0, 3, 2, 0], [1, 2, 3, 1], [1, 3, 2, 1]]`

```
allcycles = []
for array in all_dcycles:
if len(array)>=4:
reversed_array = array[::-1]
if reversed_array not in allcycles:
allcycles.append(array)
print(allcycles)
```

`[[0, 2, 1, 0], [0, 3, 1, 0], [0, 3, 2, 0], [1, 3, 2, 1], [0, 3, 2, 1, 0], [0, 2, 3, 1, 0], [0, 3, 1, 2, 0]]`

Reversing lists and eliminating all 2-cycles seems tedious. Does SageMath provide a direct command for undirected graphs to find all cycles or cycles of a specific length? It's somewhat similar to Mathematica's `FindCycle`

(`FindCycle[CompleteGraph[4], Infinity, All]`

).