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pandas.IntervalIndex.is_non_overlapping_monotonic

IntervalIndex.is_non_overlapping_monotonic

Return True if the IntervalIndex is non-overlapping (no Intervals share points) and is either monotonic increasing or monotonic decreasing, else False

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http://pandas.pydata.org/pandas-docs/version/0.23.4/generated/pandas.IntervalIndex.is_non_overlapping_monotonic.html