Where did graphs come from? (Graph Theory History) In its simplest form, Graph Theory defines a graph as a construct made up of vertices, nodes, or points which are connected by edges, arcs, or lines.1 The connections may be directed, indicating a direction from one node to another, or undirected. Properties are attributes associated with nodes that describe the node in some detail. Graph theory is applied in many disciplines from linguistics to computer science, physics, and chemistry. ...