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Enabling device-to-device (D2D) communication in cellular network is shown to be a promising candidate in the future fifth generation (5G) wireless network. Specifically, the hybrid architecture leads to flexible and efficient resource allocation for cellular users and D2D users, thereby enhancing utilization of spectrum resources. However, if not properly handled, mutual interference will be significantly raised with the proliferation of devices, which bottlenecks the performance of the hybrid system. In this paper, joint mode selection and resource allocation is considered for a sparse code multiple access (SCMA) enabled uplink cellular network. Targeting at maximizing system sum rate, we formulate a joint optimization problem, which, however, is shown to be a mixed-integer nonlinear programming (MINLP) problem. To solve the problem, we propose a graph-based joint mode selection and resource allocation (GMR …