Two topological probability rules for pattern selection in recurrent network are introduced. The first one selects patterns according to a Gibbs-type distribution. We start with a Hopfield-type dynamics on a ring model and then a Langevin model on a general random graph is treated. The phenomenon of phase transition in pattern selection motivated us to introduce an alternative topological rule for pattern selection. In a network of neurons on a random -regular graph, two asymptotic cases, and , have been discussed for the new rule, and it is shown that capacity of the network grows considerably as . By introducing the notions of asymptotic eigenvector, we will be able to study the behaviour of the discrete model in the limit . It will be proved that for degree less than a critical value there is a positive role for noise, in which case increasing the number of patterns will improve the storage capacity.