Effective non-universality of the quorum percolation model on directed graphs with Gaussian in-degree

• Collective behavior of dissociated neuronal cultures.
• Continuous prolongation of the quorum percolation model.
• Thorough numerical calculations in the infinite limit behavior.
• Accurate thresholds and critical exponent associated with the percolation transition: non universal behavior.
• Relation between critical parameters and topological properties of the network.

We investigate a model derived from bootstrap percolation on a directed random graph with Gaussian in-degree useful in describing the collective behavior of dissociated neuronal networks. By developing a continuous version of the model, we were able to provide accurate values of the critical thresholds and exponents associated with the occurrence of a giant cluster. As a main result, it turns out that the values of the exponents calculated over a numerical accessible range covering more than two orders of magnitude below the critical point exhibit a slight dependence upon the connectivity of the graph.