Probabilistic analysis of efficiency and vulnerability in the Erdös–Rénji model

Abstract

New analytic estimates for efficiency and vulnerability in the Erdös–Rénji model are presented using probabilistic properties and diameter bounds that are specific for this model and its topology. These estimates for random networks improve the known deterministic lower estimates for efficiency and vulnerability. The probabilistic technique provides a sharper approach to parametric analysis of random networks and allows us to report some new results concerning the efficiency–vulnerability relationship. Several numerical tests are presented to compare the lower estimates obtained with the empirical Erdös–Rénji random networks. These estimates illustrate how the new probabilistic estimates improve on the generic estimates reported in the literature.

Keywords:

• Computational mathematics
• Complex networks
• Mathematical modelling
• Complex systems
• Formal languages