In computing, a network generally denotes devices, often referred to as nodes, connected by links. Networks that are modeled with diagrams consist of hundreds of symbols, images, pictures, and icons, such as a computer, a server rack, or a cloud-based storage system. Network representations provide valuable insights into understanding the systems' underlying structures and mechanisms. Nevertheless, this unusually large number of superficial symbols and icons reflects a need for more systematic representations of the interiority of nodes. To give uniformity to this cascade of notions of basic units of nodes in network diagrams, the authors propose adoption of a new modeling methodology, called a thinging (abstract) machine (TM) (abstract machine of things) that represents all notions as a single diagrammatic machine. Because of the large number of network types, in this paper, they specifically and without loss of generality focus on IP telephone (internet protocol telephone) networks to exemplify communication networks. A real case study of IP telephone networks is modeled using TM.