By incorporating the merits of satellite, aerial, and terrestrial communications, the space-air-ground integrated network (SAGIN) emerges in recent years as a promising solution to support seamless, high-rate, and reliable transmission with an extremely larger coverage than a classic terrestrial network. In essence, SAGIN is a cooperative relay network, in which highaltitude platforms (HAPs) and terrestrial base stations (BSs) serve as intermediates relaying signals between end device and satellite. In this paper, we thereby view the SAGIN from the perspective of cooperative communications and introduce relay networking technologies to model and construct the framework of SAGIN. Meanwhile, we take the realistic propagation environment, HAP mobility and mathematical tractability into account and reconstruct the cooperative channel models for SAGIN, including the space-air, space-ground and air-ground links. Based on the constructed framework of SAGIN, we analyze the outage performance and approximate the outage probability as well as asymptotic outage probability in closed form. Numerical results generated by computer simulations verify our analysis and provide insight into the applicability of SAGIN. Although the relaying scenarios considered in this work are simplistic, the good tractability and expandability of the constructed framework provide a solid foundation for further research of advanced systems with complex configurations.