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Connectivity and routes in large geometric network hypergraphs
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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.
Informatization and Communication Journal Editorial Board
Title: Connectivity and routes in large geometric network hypergraphs
Description:
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.
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