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Maybe it can share the ground maybe not, it depends of the circuit you want or you did. If they share ground, yes you can conect them but if they not share ground you have to apply a diferential of potential in other, like an usb or ethernet where for the data there are two wires (one have a voltage for the other wire) because if you put just a wire without share ground there is not reference for the voltage and remember that a voltage is a potential difference.
I have two Arduinos each one is powered by a 9 volt wall plugin adapter.( I paid around 8 dollars for each plugin adapter ).
Can I connect the ground from one Arduino to the ground in the other Arduino?.