Abstract
Non-uniform hypergraphs appear in several domains of computer science as in the satisfiability problems and in data analysis. We analyze their typical structure before and near the birth of the complex component, that is the first connected component with more than one cycle. The model of non-uniform hypergraph studied is a natural generalization of the multigraph process defined in the “giant paper” [1]. This paper follows the same general approach based on analytic combinatorics. We study the evolution of hypergraphs as their complexity, defined as the excess, increases. Although less natural than the number of edges, this parameter allows a precise description of the structure of hypergraphs. Finally, we compute some statistics of the hypergraphs with a given excess, including the expected number of edges.
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de Panafieu, É. (2013). Phase Transition of Random Non-uniform Hypergraphs. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_12
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DOI: https://doi.org/10.1007/978-3-642-45278-9_12
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