Ayushi,
EDFA is usually connected through the transmission medium. What do you mean by parallel connection of EDFA?
I think you might mean using parallel branches to amplify different bands such as L and C bands.
the link has a paper that might be in your interest.
http://www.jeos.org/index.php/jeos_rp/article/viewFile/15015/1349
Hope that helps,
thanks
Mohamed Abouseif