Schizophrenia is increasingly conceived as a disorder of brain network organization or dysconnectivity syndrome. Functional MRI (fMRI) networks in schizophrenia have been characterized by abnormally random topology. We tested the hypothesis that network randomization is an endophenotype of schizophrenia and therefore evident also in nonpsychotic relatives of patients. Head movement-corrected, resting-state fMRI data were acquired from 25 patients with schizophrenia, 25 first-degree relatives of patients, and 29 healthy volunteers. Graphs were used to model functional connectivity as a set of edges between regional nodes. We estimated the topological efficiency, clustering, degree distribution, resilience, and connection distance (in millimeters) of each functional network. The schizophrenic group demonstrated significant randomization of global network metrics (reduced clustering, greater efficiency), a shift in the degree distribution to a more homogeneous form (fewer hubs), a shift in the distance distribution (proportionally more long-distance edges), and greater resilience to targeted attack on network hubs. The networks of the relatives also demonstrated abnormal randomization and resilience compared with healthy volunteers, but they were typically less topologically abnormal than the patients' networks and did not have abnormal connection distances. We conclude that schizophrenia is associated with replicable and convergent evidence for functional network randomization, and a similar topological profile was evident also in nonpsychotic relatives, suggesting that this is a systems-level endophenotype or marker of familial risk. We speculate that the greater resilience of brain networks may confer some fitness advantages on nonpsychotic relatives that could explain persistence of this endophenotype in the population.psychosis | dysconnectivity | graph theory | brain network | hubs S chizophrenia is increasingly conceived as a brain dysconnectivity syndrome or disorder of brain network organization (1-4). Various methods have been used to demonstrate abnormal structural or functional connectivity between brain regions in patients with schizophrenia. Specifically, several recent studies have used graph theory to measure the topological pattern of connections (or edges) between regional nodes in large-scale networks derived from neuroimaging data (5-12).The results to date of graph theoretical studies of schizophrenia are not entirely consistent, but there is some convergence around the concept of topological randomization (9, 13). For example, human brain networks (and many other complex, real-life networks) generally have a small-world topology that can be understood as intermediate between the regular, highly clustered organization of a lattice and the globally efficient organization of a random graph. Three independent functional MRI (fMRI) studies have shown that the functional brain networks of patients with schizophrenia are relatively shifted toward the random end of this small-world spectrum, i.e., the...