Transmission and Closeness Centrality in Networks - Jane Olive Sharon P - Bog

Discrete Mathematics is the analysis of mathematical structures that are fundamentally discrete. It is being dynamically used in the fields of arithmetic and software engineering. Graph theory deals with mathematical models referred to as graphs. It has broad applications in computer science, semantics, sociologies, factual mechanics, hereditary qualities, cheminformatics, bio-informatics and so on. Graph theory has emerged as a vital and effective tool for engineers and scientists, for example, in the area of designing and analyzing algorithms for various problems that range from designing the itineraries for a shipping company to sequencing the human genome in life sciences.

Graphs are mathematical structures which consist of a set V of vertices and set E of edges joining certain pairs of vertices. They are used to model pair-wise relations between objects from a certain collection. Vertices, also called nodes, are represented as points in the plane and edges are represented as the line segments connecting them. If more than one edge joins a pair of vertices or an edge has its origin and end as the same vertex, then such a graph is called a pseudograph.

Graphs are networks of points connected by lines. Graph theory had its beginnings in recreational puzzles and games, but it has grown into a significant area of mathematical research, with applications in chemistry, operations research, social sciences, and computer science.

The history of graph theory may be specifically traced back to 1735, when the Swiss mathematician Leonhard Euler solved the Konigsberg bridge problem. The Konigsberg bridge problem was an old puzzle concerning the possibility of finding a path over every one of the seven bridges that span a forked river flowing past an island but without crossing any bridge twice.

Graph theory is applied to simple daily life problems to very complex problems. To make this possible, computer science plays an enormous role. It depends on the theories and proofs in mathematics for developing software applications.