In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

A graph in this context is made up of vertices or nodes and lines called edges that connect them. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see graph for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics.

Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore diffusion mechanisms, notably through the use of social network analysis software. Under the umbrella of Social Network graphs there are many different types of graphs: Starting with the Acquaintanceship and Friendship Graphs, these graphs are useful for representing whether n people know each other. Next, there is the influence graph. This graph is used to model whether certain people can influence the behavior of others. Finally, there’s a collaboration graph which models whether two people work together in a particular way. The measure of an actor's prestige mentioned above is an example of this; other popular examples include the Erdős number and six degrees of separation.

A useful book that covers all relevant information related to the theory and application of Graph in easy language.

Contents:

Introduction; Reconstruction Conjecture; Ramsey Theory; Route Problems; Directed Acyclic Graphs; Algebraic Graph Theory; Bipartite Graph.