In this paper, we propose an undirected model of learning systems, named max-min-degree neural network, to realize centralized-decentralized collaborative computing. The basic idea of the proposal is a max-min-degree constraint which extends a k-degree constraint to improve the communication cost, where k is a user-defined degree of neurons. The max-min-degree constraint is defined such that the degree of each neuron lies between kmin and kmax. Accordingly, the Boltzmann machine is a special case of the proposal with kmin=kmax=n, where n is the full-connected degree of neurons. Evaluations show that the proposal is much better than a state-of-the-art model of deep learning systems with respect to the communication cost. The cost of the above improvement is slower convergent speed with respect to data size, but it does not matter in the case of big data processing.