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Electron transport and the exact scaling relations for two irreducibly coupled Aharonov-Bohm (AB) rings with two external terminals attached are investigated. In coupled AB rings, a center common path exists where the phase of the electron wave function can be modulated by two applied fluxes simultaneously. The two coupled rings can be considered as two coupled atoms where Fermi level crossings exist not only between bonding states but also between bonding and anti-bonding states when the applied flux is varied in one of the two cases studied. We show that when the smallest atomic-sized coupled rings are scaled up any odd number of times, an identical electron transmission is preserved. When two terminals are attached to isolated coupled AB rings, there is a further redistribution of bond-charge stored within the center common path. The shift of the electron charge distribution to favor one end of the common path is accompanied by the redistribution of the two partial waves that traverse through the two arms from the input to the output terminal. The flux can control which arm the electron traverses through more favorably, and hence, the center path behaves like a flux-controlled charge reservoir for the electron transport. The unbalanced charge in the entire structure creates a space-charge effect much like a p-n junction. The paradox of the delocalization of the electron wave when two AB rings are coupled and the subsequent localization effect of the electron transport in a quantum network are described.