Smart grids integrate communication systems with power networks to enable power grids operation and command through real-time data collection and control signals. Designing, analyzing, and simulating smart grid infrastructures as well as predicting the impact of power network failures strongly depend on the topologies of the underlying power network and communication system. Despite the substantial impact that the communication systems bring to smart grid operation, the topology of communication systems employed in smart grids was less studied. The power community lacks realistic generative communication system models that can be calibrated to match real-world data. To address this issue, this paper proposes a framework to generate the underlying topological graphs for the communication systems deployed in smart grids by mimicking the topology of real-world smart grids. In this regard, we have updated the Chung-Lu algorithm to guarantee the communication network connectivity and to match the degree distribution of a real-world smart grid rather than following an expected degree distribution. In addition, key characteristics of communication systems such as diameter, average shortest paths, clustering coefficients, assortativity, and spectral gap were taken into consideration to generate the most similar real-world communication network for smart grid studies. We believe that the proposed algorithm to generate realistic cyber graphs for smart grid studies will benefit the power community.