We describe and analyze a magnetic cellular nonlinear network using spin waves for information exchange. The network consists of magneto-electric cells integrated onto a common ferromagnetic film - spin wave bus. A magneto-electric cell is an artificial multiferroic comprising piezomagnetic and piezoelectric materials, which electric and magnetic polarizations entangled via the magneto-electric coupling. A bit of information is encoded into the cell's magnetic polarization, which is controlled by the applied electric field. The cell interacts with other cells not directly but via the spin waves propagating in the spin wave bus. The latter makes it possible to control the intercell communication by an external global parameter - magnetic field. We present the results of numerical modeling illustrating network performance. The utilization of spin waves offers an intrigue possibility to exploit wave phenomena at nanometer scale for building low-power dissipating and multi-functional logic deices for special task data processing. The disadvantages and shortcomings of the magnetic network with spin wave bus are also discussed.