graphs (union, intersection,

[Lindley]

Guess the numbers in a set in graphs is basically the "coordinates". Vertice in Graph has a set of (1,2), (1,4),(3,1) (3,4) where it is basiicaly saying 1 to 2 is has an edge, 1 to 4, 3,1 and 3 to 4 and each number is a vertice of the graph.

That's basically correct.

I don't know. Just hard to think of it as a graph. THink that is my road block.

The word "graph" is a bit overloaded in mathematics. You probably think of a graph as a plot of x versus y for some function. This usage of the word is completely different. (I'm sure there's a link on some level, but it's conceptually easier to start from scratch.)

A graph is a collection of vertices (singular vertex; the plural vertexes is sometimes used instead) connected by directed or undirected edges. Graphs can be represented visually but they don't have to be drawn in order to be a graph.

One example of a well-known graph algorithm is Google Maps. Every intersection on the map is a vertex; roads form edges between them. Then when you put in a starting point and destination, Google Maps uses a graph algorithm (probably Dijkstra) to compute the shortest path between those two points.