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A Monte Carlo Approach to Measure the Robustness of Boolean Networks

Emergence of robustness in biological networks is a paramount feature of evolving organisms, but a study of this property in vivo, for any level of representation such as Genetic, Metabolic, or Neuronal Networks, is a very hard challenge. In the case of Genetic Networks, mathematical models have been used in this context to provide insights on their robustness, but even in relatively simple formulations, such as Boolean Networks (BN), it might not be feasible to compute some measures for large system sizes. We describe in this work a Monte Carlo approach to calculate the size of the largest basin of attraction of a BN, which is intrinsically associated with its robustness, that can be used regardless the network size. We show the stability of our method through finite-size analysis and validate it with a full search on small networks.