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In my first talk we have seen four naturally occurring sub-graphs of complex graphs, namely the Yahoo instant messaging graph, AS-BGP network, an induced sub-graph of a collaboration graph and a sub-graph of Hollywood graph. There are many such graphs such as food-web graphs, protein-protein interaction graphs and so on and on. All these networks have a few distinct characteristics: (1) they are large (few hundreds of thousands to billons of nodes or vertices) (2) they could be dense or sparse (3) they have the “small world phenomenon” (4) they are scale free. I have discussed the first two properties and established the mathematical language to explain the last two properties in my first talk. In this talk, I will review the material covered in my first talk and explain the last two properties of complex networks. Then, we will discuss random graphs and their relevance to the complex networks. There are students present in these CREST talks, so, It will be necessary for me to start each conversation/topic from scratch as much as possible, But, some time, we have move fast, then I hope the professors can help the students to catch up. I am not yet talking about my research work since I need to lay the foundations, I will present my work in later talks.