*Topological Rankings in Communication Networks*

Andreas Aabrandt and Vagn Lundsgaard Hansen (Technical University of Denmark, Denmark); Chresten TrÃ¦holt (Technical University of Denmark)

In the theory of communication the central problem is to study how agents exchange information. This problem may be studied using the theory of connected spaces in topology, since a communication network can be modelled as a topological space such that agents can communicate if and only if they belong to the same path connected component of that space. In order to study combinatorial properties of such a communication network, notions from algebraic topology are applied. This makes it possible to determine the shape of a network by concrete invariants, e.g. the number of connected components. Elements of a network may then be ranked according to how essential their positions are in the network by considering the effect of removing them. In this paper it is shown that the topology of a given network induces a ranking of the entities in the network.

Journal: *International Journal of Simulation- Systems, Science and Technology- IJSSST V16*

Published: Feb 28, 2015