Since graphs support bidirectional references between nodes and nodes can virtually have unlimited neighbors, it is necessary to define two basic objects in order to implement the collection. These include the nodes that make up the graph as well as the graph collection itself. Optionally, an edge object may be required if the implementation supports edges that contain a value. Therefore, note that some of these common graph operations will have components in more than one class:
AddNode: This operation is sometimes called the AddVertex or AddPoint operation, and is dependent on the language used to define the graph. The AddNode operation simply inserts new nodes into the graph without defining any edges or references to neighboring nodes. Since a node does not necessarily need to have neighbors to exist in the graph, the AddNode operation represents an O(1) operation. Also note that the AddNode operation is exclusively implemented in the graph collection object.
RemoveNode...