The development and efficient application of Fog Computing technologies necessitate complex tasks associated with the management and processing of large data sets, including the creation of low-level networks that guarantee the functioning of end devices within the Internet of Things (IoT) concept. This article presents the utilization of graph theory techniques to address these issues. The proposed graph model enables the determination of fundamental characteristics of systems, networks, and network devices in Fog Computing, including optimal features and methods to maintain them in a functioning condition. This work demonstrates how to create and personalize graph displays by adding labels or highlighting to the graph nodes and edges of pseudo-random task graphs. The task graphs, described and visualized in Matlab code, represent the computational work to perform and data transfer between tasks, expressed in Megacycles per second and kilobits/kilobytes of data, respectively. The task graphs can be applied in both single-user systems, where one mobile device accesses a remote server, and multi-user systems, where many users access a remote server through a wireless channel. This set can be utilized by researchers to evaluate cloud/fog/edge computing systems and computational offloading algorithms.