In this work we analyze the mean-square performance of different strategies for adaptation over two-node least-mean-squares (LMS) networks. The results highlight some interesting properties for adaptive networks in comparison to centralized solutions. The analysis reveals that the adapt-then-combine (ATC) adaptive network algorithm can achieve lower excess-mean-square-error (EMSE) than a centralized solution that is based on either block or incremental LMS strategies with the same convergence rate.