Keys sharing Mode Formulas

Is there a Formula, that explains the correlation of, why (i.e.) 'A' Lydian also shares Harmonies of the 'B-Mixolydian, and/or, E-Ionian, ? There should be a logical way of determining each, 'Key, in any Mode, that shares other Modes... 'Circle of 5ths, & 4ths?'. If so, how to use it? ...

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