Properties of geometric hypergraphs of wireless computer networks

Mathematical models of wireless computer networks are considered, reflecting two types of interaction between nodes of the same network — broadcast and routing. A natural form of representation of such a network is a hypergraph, in which the direct links between nodes that do not require routing are specified by the hyper-edges. The routes are chains of hyper-edges. The concepts of geometric and random hypergraphs are introduced, the dependences of the probabilistic characteristics of random geometric hypergraphs on the number of vertices and radii of reliable reception / transmission of radio signals by network nodes are studied — the mathematical expectation and standard deviation of the number of hyperedges, degrees of hyperedges. The properties of dynamic geometric hypergraphs are discussed, their influence on the connectivity of a computer network, and the requirements for algorithms for managing connectivity in terms of hypergraphs are formulated.