Nodes are useful for implementing ADTs, but is "node" itself an ADT? How does one implement "node"? Wikipedia uses a plain old struct with no methods in its (brief) article on nodes. I googled node to try and find an exhaustive article on them, but mostly I found articles discussing more complex data types implemented with nodes.
Just what is a node? Should a node have methods for linking to other nodes, or should that be left to whatever owns the nodes? Should a node even be its own standalone class? Or is it enough to include it as an inner struct or inner class? Are they too general to even have this discussion?
A node is an incredibly generic term. Essentially, a node is a vertex in a graph - or a point in a network.
In relation to data structures, a node usually means a single basic unit of data which is (usually) connected to other units, forming a larger data structure. A simple data structure which demonstrates this is a linked list. A linked list is merely a chain of nodes, where each node is linked (via a pointer) to the following node. The end node has a null pointer.
Nodes can form more complex structures, such as a graph, where any single node may be connected to any number of other nodes, or a tree where each node has two or more child nodes. Note that any data structure consisting of one or more connected nodes is a graph. (A linked list and a tree are both also graphs.)
In terms of mapping the concept of a "node" to Object Oriented concepts like classes, in C++ it is usually customary to have a Data Structure class (sometimes known as a Container), which will internally do all the work on individual nodes. For example, you might have a class called LinkedList. The LinkedList class then would have an internally defined (nested) class representing an individual Node, such as LinkedList::Node.
In some more cruder implementations you may also see a Node itself as the only way to access the data structure. You then have a set of functions which operate on nodes. However, this is more commonly seen in C programs. For example, you might have a struct LinkedListNode, which is then passed to functions like void LinkedListInsert(struct LinkedListNode* n, Object somethingToInsert);
In my opinion, the Object Oriented approach is superior, because it better hides details of implementation from the user.