Network science provides tools to explore the overall organization of the human functional brain as a consequence of wiring dynamics, offering new insights on the effect of abnormal functioning on the whole brain network architecture [1]. In this perspective, Schizophrenia represents an interesting case study: a severe psychiatric condition hypothesized to result from abnormal anatomical neural connectivity and a consequent decoupling of the brain’s integrative thought processes [2]. Recently, it has been proposed a procedure to investigate on the skeleton of the healthy brain functional connectedness [3]. Here we apply the same techniques to compare the resting state functional magnetic resonance imaging (rs-fMRI) data from forty-four schizophrenic (SZ) and forty healthy subjects (HS). Experimental details and the full preprocessing of data are described elsewhere [3]. The human brain was segmented into 116 regions according to the AAL template [4]. Resting state fMRI signals were averaged across each region to generate 116 time-series (nodes), pairwise correlated (link edge) [3]. First, the percolation curve, calculated for both HS and SZ, revealed that SZ functional networks resist to disconnection much more than HS ones (fig.1(a)).This can be interpreted as a lack of flexibility of functional plasticity, which, in turn, may induce a dysfunctional integration among neuronal systems [5]. Second, we computed the Maximum Spanning Tree (MST) of the correlation matrix for each subject in the two groups. Then, we removed from the initial correlation matrix all links corresponding to such MST and computed a novel MST. We repeated the procedure several times. For each MST we computed Ai, the number of nodes in the subtree having i as root and Ci=∑kAk. In both river and vascular networks, the shape of Ci as a function of Ai, the allometric slope,is universal and optimised [6]. Here, we find for each subject a power-law scaling of the form C∝Aη . Results show that, starting from a quite similar condition, the power-law exponent in HS tend to reduce faster than in SZ by removing links (fig.1(b)). In general η∊(1,2], with boundaries associated to extreme configurations: star-like and chain-like [6]. Since for both groups of subjects the allometric slope associated to the first MST (the original backbone) is close to 1.5, we can say it represents the more stable configuration of the functional architecture. Results suggest that SZ functional networks are characterized by more stable configurations: at each stage the allometric slope values are closer to 1.5 than those coming from the HS trees. This outcome may depend on an excess of synaptic connections that survived to the expected cortical pruning [7].
