Connectivity and routes in large geometric network hypergraphs

Random geometric hypergraphs are considered as mathematical models of large wireless computer networks. The dependences of the mathematical expectation of the number of hyper-edges in random geometric hypergraphs on the radii of reliable reception / transmission of radio signals by network nodes, as well as on the number of vertices in the hyper- graph are studied. The concepts of the shortest route in a geometric hypergraph are discussed. Calculations of the probabil- ity of connectivity of large random geometric hypergraphs, the mathematical expectation of the diameter of hypergraphs and its change with a change in the radii of the nodes are carried out. The presentation of the results is accompanied by graphs.