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We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding hyper-edge. It defines a random hyper-multigraph specified by two distributions, one for the degrees of the vertices, and one for the sizes of the hyper-edges. We develop the logical analysis of this framework and first prove a convergence law for first-orderarXiv:1501.07429v3 fatcat:bekcrtkkbrfanjgxwdzqk5b2vy