Finding cycles in graphs is a computationally difficult task. Nevertheless, published ecosystems contain a few hundred nodes at most, and the low connectance (fraction of realized connections) displayed by these systems ensures that the number of simple cycles is much lower than the theoretical case illustrated above, where all possible cycles are present.
The idea behind most algorithms for cycle search is simple: one should construct a path inside the network until the same node is found twice. In this case the path is either a cycle (the initial and final nodes do coincide) or a compound path (initial and final nodes are different).
Of the various possible ways of searching the cycles, backtracking-based ones, such as 'depth first search' (DFS) are surely the easiest to implement.
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