In this chapter the concept of graphs is taken up and formalized. For this purpose, an abstract data type is presented as an interface that describes graphs and is extended to an interface for distributed graphs. The reason for this is obvious: A network conceptually represents an undirected graph. The processes on the participating computers, uniquely defined by their name or IP address, form its vertices and the communication paths between them—realized by network lines, e.g., Ethernet cables, and the programs that enable the network traffic—the transport of messages over the network, e.g., by TCP/IP, form its edges. The following chapters will show that many distributed algorithms fit exactly into this framework.