What is Graph Theory

Definition: Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.

Description: A graph ‘G’ is a set of vertex, called nodes ‘v’ which are connected by edges, called links ‘e'. Thus G= (v , e).
Vertex (Node): A node v is an intersection point of a graph. It denotes a location such as a city, a road intersection, or a transport terminal (stations, harbours, and airports).


Edge (Link): An edge e is a link between two nodes. A link denotes movements between nodes. It has a direction that is generally represented as an arrow. If an arrow is not used, it means the link is bi-directional.

Transport geography can be defined by a graph. Most networks, namely road, transit, and rail networks, are defined more by their links than by nodes. But it is not true for all transportation networks. For instance, air networks are defined more by their nodes than by their links since links are mostly not clearly defined. A telecommunication system can also be represented as a network. Mobile telephone networks or the internet is the considered the most complex graph. However, cell phones and antennas can be represented as nodes whereas links could be individual phone calls. The core of the internet or servers can also be represented as nodes while the physical infrastructure between them, like fiber optic cables, can act as links. This suggests that all transport networks can be represented by graph theory in some way.