This paper highlights the most important benchmarks in the recent research history of network science.In particular, I address the network topology of the so-called Erdős and Rényi network in terms of the network model they developed to describe random networks. Subsequently, I discuss the emerging limitations of this model in regard to real networks. Accordingly, I address on the extension of the Erdős-Rényi network by Watts and Strogatz. Due to the emergence and development of the world-wide-web and social networks as a consequence, a new topology and properties of networks have emerged in the research area of Network Science, which will be discussed using the Barabási-Albert model.