Graph Representation of a Real Network

The goal of a graph is to represent the structure, not the appearance of a network. The conversion of a real network into a planar graph is a straightforward process that follows some basic rules:

• The most important rule is that every terminal and intersection point becomes a node.
• Each connected node is then linked by a straight segment.

The outcome of this abstraction, as portrayed in the above figure, is the actual structure of the network. Depending on its complexity, the real network may be confusing in terms of revealing its connectivity (what is linked to what). A graph representation reveals the connectivity of a network in the best possible way. Other rules can also be applied, depending on the circumstances:

• A node that is not a terminal or an intersection point can be added to the graph if, along that segment, an attribute is changing. For instance, it would be recommended to represent the shift from 2 lanes to 4 lanes along a continuous road segment as a node, even if that shift does not occur at an intersection or terminal point.
• A “dummy node” can be added for esthetical purposes, especially when the shape of the graph representation is required to be comparable to the real network.
• Although the relative location of each node can remain similar to its real-world counterpart (as in the above figure), this is not required. It is, however, a preferred option to help understand the geographical context of the network being represented.