Analysis of Routing Entropy in Hyperbolic Trees

Recent results have shown that the memory requirements of destination-based hop-by-hop routing in largescale communication networks can efficiently be estimated by the information theoretic!! entropy of the forwarding tables placed at the nodes. For calculating and analyzing the memory usage the forwarding tables are to be inferred according to the routing algorithm, then the entropy values can be established. This could be a computationally intensive task, especially in case of large networks operated along complex routing policies making the analysis hard and less tractable. In this paper we focus on a special case, when the routing is based on a spanning tree the so called hyperbolic tree. We show that the routing entropy can efficiently be computed in this case without generating the forwarding tables. Based on this computation, analytical results on routing scalability with respect to memory usage can also be derived, which confirms observations on numerical investigations. These network theoretical results will expectedly have significance in the forthcoming 5th generation (5G) and the future 6th generation (6G) complex communication systems. The representation and modelling power of hyperbolic complex networks may greatly help in mastering the complexity of rapidly expanding systems like 5G and 6G communication networks.