Convergence law for hyper-graphs with prescribed degree sequences [article]

Nans Lefebvre
2015 arXiv   pre-print
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-order
more » ... gic, then characterise the limit first-order theories defined by a wide class of degree distributions. Convergence laws of other models follow, and in particular for the classical Erdős-Rényi graphs and k-uniform hyper-graphs.
arXiv:1501.07429v3 fatcat:bekcrtkkbrfanjgxwdzqk5b2vy