Graph Theory is the mathematical study of the properties and applications of graphs. Graphs are mathematical structures used to model pairwise relations between objects. Graphs are also referred to as networks and contain a set of vertices/nodes/points connected by edges/links/lines.
Graph Theory was first introduced and studied in 1736 by Leonhard Euler who was interested in solving the Konigsberg Bridge Problem. Konigsberg was a city in Prussia, Russia with the river Pregel flowing through it creating two islands. The city and islands were connected by seven bridges. The goal of the Konigsberg Bridge Problem was to devise a walk through the city that would cross each of the 7 bridges once and only once with no doubling back, ensuring that you ended where you started.
One way of utilizing Graph Theory in Network Analysis is by using a powerful python library called NetworkX. NetworkX is a python language software package and an open-source tool for the creation, manipulation and study of the structure, dynamics and functions of complex networks.
The following python code will provide an in depth illustration of how Graph Theory can be used in Network Analysis. It will be applied to Airport Data where the nodes are Airport Abbreviations and the edges represent the Distance between those Airports.
NetworkX is a powerful python library that can be used to experiment with Graph Theory and Network Analysis. It is a strong tool for studying the connections between nodes and can be used to derive statistics that pull out useful information about the structure, distribution and dynamic of a Graph.