A distributed geometric rewiring model

Abstract

We propose a distributed rewiring model which starts with a planar graph embedded into the Euclidean space and then behaves as a distributed system, where each node is provided with a set of dynamic links. The proposed rewiring evolves through cycles, where nodes explore the network to identify possible shortcuts and rewire their dynamic links. The rewiring decisions are subject to Euclidean and geodesic distance constrains. The emerging networks were assessed through topological and robustness analyses. We found that the networks display a variety of characteristics observed in complex networks encompassing phenomena such as preferential attachment, the distinctive traits of small-world networks, the presence of community structures, and robustness against degradation process. We consider that our proposal can be applied in the design of those self-managed systems in which there is a limitation on communication resources that can be represented by the Euclidean distance and, however, the components themselves can deploy strategies to optimize the transport of information and develop tolerance before contingencies.