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The approach of factor-graphs (FGs) is applied in the context of power control and user pairing in Device-to-Device (D2D) communications as an effective underlay concept in wireless cellular networks. D2D communications can increase the spectral efficiency of wireless cellular networks by establishing a direct link between devices with limited help from the evolved node base stations (eNBs). A well-designed user pairing and power allocation scheme with low complexity can remarkably improve the system's performance. In this paper, a simple and distributed FG based approach is utilized for power control and user pairing implementation in an underlay cellular network with D2D communications. A max-min criterion is proposed to maximize the minimum rate of all active users in the network, including the cellular and multiple D2D co-channel links in the uplink direction. An associated message-passing (MP …