Centrality of nodes in Federated Byzantine Agreement Systems

The federated Byzantine agreement system (FBAS) is a consensus model introduced by Mazi\`eres in 2016 where the participating nodes conceptually form a network, with links between them being established by each node individually and thus in a decentralized way. An important question is whether these decentralized decisions lead to an overall decentralized network. The level of (de-)centralization in a network can be assessed using centrality measures. In this paper we consider three different approaches for obtaining centrality measures for the nodes in an FBAS. Two of them are based on adapting well-known measures based on graphs and hypergraphs to the FBAS context. Since the network structure of an FBAS can be more complex than (usual) graphs or hypergraphs, we also develop a new, problem-adapted centrality measure. This new measure is based on the intactness of nodes, which is an important ingredient of the FBAS model. We illustrate advantages and disadvantages of the three approaches on several computed examples. We have implemented all centrality measures and performed all computations in the Python package Stellar Observatory.