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Graphs. Most people identify this phrase with a statistical graph, such as a bar, line, circle or a graph of a function. But, the analysis of graphs is referred to as graph theory in mathematics. Graphs are a central topic in discrete mathematics. Graphs, which are comprised of vertices (nodes or actors) and edges (links), are used as models in graph theory. These mathematical models represent real-world problems and circumstances. The concept of graph theory is derived from a mathematical depiction of this type of situation. In mathematics, graph theory is an exciting and dynamic field. It is used to examine real-world challenges in various fields ranging from chemistry to linguistics, geography to sociology, transportation to infrastructure networks, social science to biological networks and so on. Graphs are mathematical constructions used to represent pair wise relationships between objects. They can be found on maps, in constellations and in the design and drafting process. Graphs highlight various computer applications that enable modem communication and technological processes. They serve to strengthen logical and abstract thinking. Graph theory emerged as an academic discipline in 1736, when Leonhard Euler solved the renowned Konigsberg bridge issue. Euler solved the Konigsberg bridge problem by expressing it as a graph theory problem, with the land areas represented as vertices and the bridges as edges. Euler introduced the concept of degree by stating that if a graph has no more than two odd vertices, then there exists some path that traverses each edge once. Complex network graphs differ greatly from ordinary graphs. Network science is the study of complex networks, which can represent any distinct system, from different interaction networks to social networks. Over the last two decades, network research has contributed to the identification of universal and surprising patterns in a wide range of domains, from ecological and social systems to technical and biological systems. From the research of last two decades in various domains, it will help to create innovative multidisciplinary tools for transforming many real world problems into models so that it can easily solvable.