Diffusion fused sparse LMS algorithm over networks

•We derive the fused sparse diffusion algorithm to recover sparse parameter by enforcing sparsity of components themselves and similarity of adjacent components.•We provide the condition of convergence in the mean sense.•We study mean-square behavior and provide the expressions for calculating network steady-state MSD and steady-state individual weight error variance (IWEV).•Numerical simulations show that our proposed algorithm is able to achieve lower steady-state MSD than several other existing algorithms in both stationary and non-stationary environments.