In this article we will give a small introduction to the discrete mathematics and its application in network analysis. Because of limitations regarding this article (extended summary) and because we are aware that the scientific study of networks, such as computer networks, biological networks, and social networks, is an interdisciplinary field that combines ideas from mathematics, physics, biology, computer science, the social sciences, and many other areas, we will try to describe some basic types of networks studied by present–day science as well as some techniques used to determine their structure.