[BUG] cycle_basis not returning the correct number of cycles

Description of bug
The cycle_basis without root parameter has a problem with a graph in the shape of the following molecule: https://pubchem.ncbi.nlm.nih.gov/compound/149096
With root, the result is inconsistent depending on the root: Mostly 3 and sometimes the correct 4 cycles smaller than 10, see below.

How to reproduce
The BiochemicalAlgorithms.jl provides a core for loading 3D Conformers from the PubChem .json format.
Download the 3D Conformer via "Download" from: https://pubchem.ncbi.nlm.nih.gov/compound/149096#section=3D-Conformer
Add the BiochemicalAlgorithms.jl package from https://github.com/hildebrandtlab/BiochemicalAlgorithms.jl (the develop branch is sufficient for this purpose). Then in Console load the molecule:
mol_149096 = load_pubchem_json("your/path/here.json")[1]

Then build the graph with the following function:
function build_graph(mol::Molecule)
mol_graph = SimpleGraph(nrow(mol.atoms))
for i = (1:nrow(mol.bonds))
add_edge!(mol_graph, mol.bonds.a1[i], mol.bonds.a2[i])
end
return mol_graph
end

After building the graph of the molecule and naming it mol_graph_CID_149096:
filter(x -> lastindex(x) < 10, cycle_basis(mol_graph_CID_149096))

Expected behavior
filter(x -> lastindex(x) < 10, cycle_basis(mol_graph_CID_149096))
Should return 4 cycles smaller than 10:
[7, 20, 25, 23, 18, 13]
[14, 12, 19, 21, 18, 13]
[9, 15, 8, 16, 10, 6]
[7, 11, 17, 2, 14, 13]

Actual behavior
Only returns 3 cycles smaller than 10:
[13, 14, 12, 19, 21, 18]
[13, 7, 11, 17, 2, 14]
[9, 15, 8, 16, 10, 6]

Code demonstrating bug
see "How to reproduce" section above

Version information
Graphs.jl v1.7.4

Additional context
Add any other context about the problem here.

Start at the cycle_basis entry point in Graphs.jl and reproduce the issue using the PubChem compound 149096 graph described above. Compare results with and without the root parameter, including the listed cycle-size filter; done means the reproduction returns all 4 expected cycles smaller than 10 consistently.