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The Tutte polynomial is an important tool in graph theory. This paper provides an introduction to the two-variable polynomial using the spanning subgraph and rank-generating polynomials. The equivalency of definitions is shown in detail, as well as evaluations and derivatives. The properties and examples of the polynomial, i.e. the universality, coefficient relations, closed forms and recurrence relations are mentioned. Moreover, the thesis contains the connection between the dichromate and other significant polynomials.
Social media platforms play an increasing role in marketing, politics and police affairs, because they can strongly influence opinions. So called “opinion leaders” exert their influence in a given network and shape the opinions of other users. Identifying central nodes in a social graph has been of interest for decades. However, not all centrality measures were developed for social media platforms. They were built for social graphs, which did not include additional metrics (e.g. “likes”, “shares”). Nevertheless, these metrics play a crucial role on modern platforms. Hence, outdated measures need to be adjusted and additional metrics need to be integrated to ensure the best possible results.