A tree only allows a node to have children, and there cannot be any loops in the tree, with a more general graph we can represent many different situations. A very common example used is flight paths between cities. If there is a flight between city A and city B there is an edge between the cities. The cost of the edge can be the length of time that it takes for the flight, or perhaps the amount of fuel used.
The way that we will represent this is to have a concept of a node (or vertex) that contains links to other nodes, and the data associated with that node. So for our flight path example we might have the name of the airport as the node data, and for every flight leaving that city we have an element in neighbors that points to the destination.
structure node [list of nodes] neighbors [data] end cost(X, Y) := if (X.neighbors contains Y) return X.neighbors[Y]; else "Not possible" list nodes;
This is a very general way to represent a graph. It allows us to have multiple edges from one node to another and it is a very compact representation of a graph as well. However the downside is that it is usually more difficult to work with than other representations.