Importance of Graph Theory

In 1736, by solving a riddle of the seven bridges of Konigsberg, Leonhard Euler creates graph theory. Graphs, defined as a collection of nodes and edges linking nodes together, gives people the power to simplify problems by removing all extraneous details. Hence, graphs provide clear diagrams with many robust applications to physics and Electrical Engineering, Computer science, sociology and transportation.

A graph representation of a circuit, each edge also has an additional symbol to represent a circuit component

In physics and electrical engineering, graphs reduce Electrical Circuits into clear and simple diagrams. Each node represents a terminal on which components are connected to and each edge represents a component such as a resistor, LED or even a transistor. Graphs not only helps researchers and engineers design new circuits but analyze them for potential flaws, errors and areas that can be optimized.

In computer science it is applied to networks as well as different data structures. In networks a node can represent a computer terminal and an edge a wire connecting them. This simplification allows better analysis, strengths and weaknesses and categorization of different shapes of networks such as the star network and the fully connected network. In data structures graphs allow one to see different ways that data can be organized and accessed. Graph representations of these structures give necessary clairvoyance and analysis before they are ultimately incorporated into programs.

A graph representation of the B-Tree data structure. This structure is widely used for storing data in hard-drives and databases because it allows quick random access on these storage medium. Each node here represents a packet of data.

In sociology graphs can be used to represent interpersonal relationships, with each node representing a person and each edges is a relationship between that people. This can range from family trees to how people are connected with one another via social media.

Graphs also boast some of the world’s most famous open problems such as the Hamiltonian cycle problem and the traveling salesman problem. If it can be proven that any of these problems can have a fast algorithm, it would not make advancements in problems such as P vs NP but also revolution, trade, travel and commerce. Not only that but maps can also be simplified into modified graphs called weighted graphs, here each node represents a location while each edge has a number to represent the distance or cost for traveling form one location to another.

In conclusion through graph theory started as a way to explain a local riddle, it is today a robust field with applications to many of modern society’s most necessary fields of research.

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