Black tiles and black circles and yellow tiles are white circles...
First of all some simple deductions:
Next if R4C8 is B then it will lead to opposite pairs and so it must be W and then some more deductions:
Next if R8C5 is both B and W then it leads to these overlapping deductions so this must be the configurations...
Then if R4C4 is W then it will lead R3C5 to become isolated. So it must be black. Then a few deductions later we have:
Then using the edge rule and hypothetically say R1C8 is W then it will lead to this:
And if we say it is black it will lead to this. Notice how similar they are since alot of the deductions overlap meaning that most of this will be in the final answer.
So lets say R1C8 is W then the puzzle is unsolvable because R10C3 needs to connect to R7C5, R7C7, R6C9. And doing so will isolate a group of White circles. Therefore R1C8 must be black.
So assuming 10C4 is white and using the edge connection rule and a few deductions we have this. The finished result.