We propose an adaptive diffusion strategy with limited communication overhead by cutting off all links but one for each node in the network. We keep the “best” neighbor that has the smallest estimated variance-product measure and ignore the other neighbors. The combination coefficients for the interacting nodes are calculated via a maximal-ratio-combining rule to minimize the steady-state meansquare-deviation. Simulation results illustrate that, with less communication overhead and less computations, the proposed algorithm performs well and outperforms other related methods with similar overheads.