Graph Theory is an independent discipline of Mathematics that connects many disciplines of Mathematics together in more pragmatic approaches. The novel work of graph theory was inspired by unwavering efforts to fathom and resolve day-to-day problems in a more logical perspective. Graphs stand or fall by their choice of nodes and edges. This chapter deals with the concepts of Graphs, types of graphs, operations of graphs, isomorphism of graphs, connectivity of graphs, coloring of graph attributes, matrix representation of graphs and various algorithms for finding the shortest path. This chapter follows the concept of the “BEIMI” to define various concepts of graphs and find out the associated applications. The chapter culminates in case studies, projects and pedagogical exercises aimed at reconciling theoretical relational frameworks with their multidisciplinary practical implementations.