Scale-Free Networks: Power Laws and Preferential Attachment

This lecture covers the concepts of scale-free networks, power laws, and preferential attachment. It explains the Pareto Law, degree distributions, the Barabasi-Albert Model, and the Simon model. The lecture delves into the implementation of the Preferential Attachment rule, different versions of the Barabasi-Albert Model, and the expected node degree. It also discusses alternative approximations using Continuum Theory, assortativity in networks, and the size of the Giant component. The lecture concludes with a critique of scale-free networks and a comparison between Power Law and Lognormal distributions.