This simple concept can be represented abstractly as a graph of nodes, since theoretically a network is a graph. This allows graph theory to be applied to networking in general.
Vertices are the nodes on the graph.
Edges are the paths or links connecting two nodes. The set of edges is represented as a set of ordered pairs. The graph above is directed, meaning each edge has only one link direction, thus each edge is represented as an ordered pair. Some graphs are bi-directional much as in a network where communication between two computers can be simultaneous. The set of edges for such graphs is by unordered pairs.