Here are some options for the solvers. The current defaults for a given solver may be accessed like so:
i1 : options monodromySolve
o1 = OptionTable{AugmentEdgeCount => 0 }
AugmentGraphFunction => null
AugmentNodeCount => 0
AugmentNumberOfRepeats => null
BatchSize => infinity
EdgesSaturated => false
Equivalencer => null
FilterCondition => null
GraphInitFunction => completeGraphInit
new tracking routine => true
NumberOfEdges => 4
NumberOfNodes => 2
NumberOfRepeats => 10
Potential => null
Randomizer => null
SelectEdgeAndDirection => selectFirstEdgeAndDirection
StoppingCriterion => null
TargetSolutionCount => null
Verbose => false
o1 : OptionTable
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The object MonodromySolverOptions is a symbol.