Psychiatric illnesses characterized by disorganized cognition, such as schizophrenia, have been described in terms of fragmentation and hence understood as reduction in functional brain connectivity, particularly in prefrontal and parietal areas. However, as graph theory shows, relatively small numbers of nonlocal connections are sufficient to ensure global coherence in the modular small-world network structure of the brain. We reconsider fragmentation in this perspective. Computational studies have shown that for a given level of connectivity in a model of coupled nonlinear oscillators, modular small-world networks evolve from an initially random organization. Here we demonstrate that with decreasing connectivity, the probability of evolving into a modular small-world network breaks down at a critical point, which scales to the percolation function of random networks with a universal exponent of α = 1.17. Thus, according to the model, local modularity systematically breaks down before there is loss of global coherence in network connectivity. We, therefore, propose that fragmentation may involve, at least in its initial stages, the inability of a dynamically evolving network to sustain a modular small-world structure. The result is in a shift in the balance in schizophrenia from local to global functional connectivity.

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Coupled map networks evolve from sparsely connected random graphs to smallworld networks according to a simple adaptive rewiring algorithm. This evolution is known to occur for networks of a constant number of units and connections, and system parameters, including uniform connection strength, if the maps are chaotic. The present study investigates the consistency of the generated structures. Evolution to small-world networks is shown to occur over a wide range of network sizes above a certain threshold. The distribution of the connections reveals hierarchical structures for larger networks. In spite of high variability in the number of connections of each unit, for a given network size the number of clusters evolving shows a remarkable uniformity.

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