What is a graph, and what are some applications of graphs?

According to Wikipedia, graph is an abstract data type. And, the definition of extract data type is that it is a mathematical model of some data structure. This means that its data type depends on graph and hyper graph.
A labeled graph of 6 vertices and 7 edges. Source: Wikipedia

Basically, graph is an arc that connects significant ordered pairs assuming that each order pair as a node. That arc helps user to see the patterns of the data and helps to simplify data graphically. These graphs can be used to represent a network of roads, the relationship between people (For instance, it is used in Facebook to see how people are connected with each other.) inside the computer. Graphs can be created in many ways and a good choice of mechanism of creating a graph depends on the operation that the computer program needs to perform on the graph to achieve its needs.