The large-scale networks present in real world applications have multiple special properties that simple random graphs do not, for e.g. the small world phenomenon and scale-freeness. Therefore we need special algorithms to generate "real world" random graphs. One of the possible methods is the Barabási-Albert model detailed in this paper.
The generation of "real world" hypergraphs hasn't been researched as excessively as "real world" graphs. I present two approaches: one is based on finding the communities in a graph, the other generates the hypergraph directly. I used multiple methods to find the communities in a given graph: listing the maximal cliques (Bron-Kerbosh algorithm), k-clique percolation (Palla), iterative k-clique percolation based on the strict clique overlap criterion (Zahoránszky), and information communities (Zubcsek). I examined and evaluated the degree and edge size distribution of the generated hypergraphs.
I present a simple, graph-based epidemic model and its generalisation using hypergraphs. I show the details of their implementations, and examine and evaluate the results of the simulations based on multiple graphs and hypergraphs.