Author Summary Mapping the routing of spikes through local circuitry is crucial for understanding neocortical computation. Under appropriate experimental conditions, these maps can be used to infer likely patterns of synaptic recruitment, linking activity to underlying anatomical connections. Such inferences help to reveal the synaptic implementation of population dynamics and computation. We compare a number of standard functional measures to infer underlying connectivity. We find that regularization impacts measures heterogeneously, and that individual algorithms have unique biases that impact their interpretation. These biases are nonoverlapping, and thus have the potential to mitigate one another. Combining individual algorithms into a single ensemble method results in a stronger inference algorithm than the best individual component measure. Ensemble-based inference can yield higher sensitivity to underlying connections and an improved estimate of the true statistics of synaptic recruitment. Abstract A promising alternative to directly measuring the anatomical connections in a neuronal population is inferring the connections from the activity. We employ simulated spiking neuronal networks to compare and contrast commonly used inference methods that identify likely excitatory synaptic connections using statistical regularities in spike timing. We find that simple adjustments to standard algorithms improve inference accuracy: A signing procedure improves the power of unsigned mutual-information-based approaches and a correction that accounts for differences in mean and variance of background timing relationships, such as those expected to be induced by heterogeneous firing rates, increases the sensitivity of frequency-based methods. We also find that different inference methods reveal distinct subsets of the synaptic network and each method exhibits different biases in the accurate detection of reciprocity and local clustering. To correct for errors and biases specific to single inference algorithms, we combine methods into an ensemble. Ensemble predictions, generated as a linear combination of multiple inference algorithms, are more sensitive than the best individual measures alone, and are more faithful to ground-truth statistics of connectivity, mitigating biases specific to single inference methods. These weightings generalize across simulated datasets, emphasizing the potential for the broad utility of ensemble-based approaches.

The unique architecture of the human connectome is defined initially by genetics and subsequently sculpted over time with experience. Thus, similarities in predisposition and experience that lead to similarities in social, biological, and cognitive attributes should also be reflected in the local architecture of white matter fascicles. Here we employ a method known as local connectome fingerprinting that uses diffusion MRI to measure the fiber-wise characteristics of macroscopic white matter pathways throughout the brain. This fingerprinting approach was applied to a large sample ( N = 841) of subjects from the Human Connectome Project, revealing a reliable degree of between-subject correlation in the local connectome fingerprints, with a relatively complex, low-dimensional substructure. Using a cross-validated, high-dimensional regression analysis approach, we derived local connectome phenotype (LCP) maps that could reliably predict a subset of subject attributes measured, including demographic, health, and cognitive measures. These LCP maps were highly specific to the attribute being predicted but also sensitive to correlations between attributes. Collectively, these results indicate that the local architecture of white matter fascicles reflects a meaningful portion of the variability shared between subjects along several dimensions. Author Summary The local connectome is the pattern of fiber systems (i.e., number of fibers, orientation, and size) within a voxel, and it reflects the proximal characteristics of white matter fascicles distributed throughout the brain. Here we show how variability in the local connectome is correlated in a principled way across individuals. This intersubject correlation is reliable enough that unique phenotype maps can be learned to predict between-subject variability in a range of social, health, and cognitive attributes. This work shows, for the first time, how the local connectome has both the sensitivity and the specificity to be used as a phenotypic marker for subject-specific attributes.

Author Summary Parkinson’s disease (PD) patients with amnestic mild cognitive impairment (e.g., primary processing-speed impairments or primary memory impairments) are at greater risk of developing dementia. Recent evidence suggests that patients with PD and mild cognitive impairment present an altered connectome connectivity. In this work, we further explore the structural connectome of PD patients to provide clues to identify possible sensitive markers of disease progression, and cognitive impairment, in susceptible PD patients. We employed a weighted network framework that yields more stable topological results than the binary network framework and is robust despite graph density differences, hence it does not require thresholding to analyze the connectomes. As Supplementary Information (Colon-Perez et al., 2017), we include databases sharing the results of the network data. Abstract In this study, we investigate the organization of the structural connectome in cognitively well participants with Parkinson’s disease (PD-Well; n = 31) and a subgroup of participants with Parkinson’s disease who have amnestic disturbances (PD-MI; n = 9). We explore correlations between connectome topology and vulnerable cognitive domains in Parkinson’s disease relative to non-Parkinson’s disease peers (control, n = 40). Diffusion-weighted MRI data and deterministic tractography were used to generate connectomes. Connectome topological indices under study included weighted indices of node strength, path length, clustering coefficient, and small-worldness. Relative to controls, node strength was reduced 4.99% for PD-Well ( p = 0.041) and 13.2% for PD-MI ( p = 0.004). We found bilateral differences in the node strength between PD-MI and controls for inferior parietal, caudal middle frontal, posterior cingulate, precentral, and rostral middle frontal. Correlations between connectome and cognitive domains of interest showed that topological indices of global connectivity negatively associated with working memory and displayed more and larger negative correlations with neuropsychological indices of memory in PD-MI than in PD-Well and controls. These findings suggest that indices of network connectivity are reduced in PD-MI relative to PD-Well and control participants.

The intricate connectivity patterns of neural circuits support a wide repertoire of communication processes and functional interactions. Here we systematically investigate how neural signaling is constrained by anatomical connectivity in the mesoscale Drosophila (fruit fly) brain network. We use a spreading model that describes how local perturbations, such as external stimuli, trigger global signaling cascades that spread through the network. Through a series of simple biological scenarios we demonstrate that anatomical embedding potentiates sensory-motor integration. We find that signal spreading is faster from nodes associated with sensory transduction (sensors) to nodes associated with motor output (effectors). Signal propagation was accelerated if sensor nodes were activated simultaneously, suggesting a topologically mediated synergy among sensors. In addition, the organization of the network increases the likelihood of convergence of multiple cascades towards effector nodes, thereby facilitating integration prior to motor output. Moreover, effector nodes tend to coactivate more frequently than other pairs of nodes, suggesting an anatomically enhanced coordination of motor output. Altogether, our results show that the organization of the mesoscale Drosophila connectome imparts privileged, behaviorally relevant communication patterns among sensors and effectors, shaping their capacity to collectively integrate information. Author Summary The complex network spanned by neurons and their axonal projections promotes a diverse set of functions. In the present report, we study how the topological organization of the fruit fly brain supports sensory-motor integration. Using a simple communication model, we demonstrate that the topology of this network allows efficient coordination among sensory and motor neurons. Our results suggest that brain network organization may profoundly shape the functional repertoire of this simple organism.

Author Summary Diffusion tractography has been proven to be a promising noninvasive technique to study the network properties of the human brain. However, how various tractography and network construction parameters affect network properties has not been studied using a large cohort of high-quality data. We utilize data provided by the Human Connectome Project to characterize the changes to network properties induced by varying the brain parcellation atlas scales, the number of reconstructed tractography tracks, and the degree of grey matter dilation with graph metrics. We illustrate the importance of increasing the reconstructed track sampling rate when higher atlas scales are used. In addition to changing the raw values of graph metrics, we find that the ranks of individuals relative to the population metric distributions are altered. We further discuss how the dependency of graph metric ranks can affect the brain characteristics derived in group comparison studies using network neuroscience techniques. Abstract Network neuroscience leverages diffusion-weighted magnetic resonance imaging and tractography to quantify structural connectivity of the human brain. However, scientists and practitioners lack a clear understanding of the effects of varying tractography parameters on the constructed structural networks. With diffusion images from the Human Connectome Project (HCP), we characterize how structural networks are impacted by the spatial resolution of brain atlases, total number of tractography streamlines, and grey matter dilation with various graph metrics. We demonstrate how injudicious combinations of highly refined brain parcellations and low numbers of streamlines may inadvertently lead to disconnected network models with isolated nodes. Furthermore, we provide solutions to significantly reduce the likelihood of generating disconnected networks. In addition, for different tractography parameters, we investigate the distributions of values taken by various graph metrics across the population of HCP subjects. Analyzing the ranks of individual subjects within the graph metric distributions, we find that the ranks of individuals are affected differently by atlas scale changes. Our work serves as a guideline for researchers to optimize the selection of tractography parameters and illustrates how biological characteristics of the brain derived in network neuroscience studies can be affected by the choice of atlas parcellation schemes.

Characterizing anesthesia-induced alterations to brain network dynamics provides a powerful framework to understand the neural mechanisms of unconsciousness. To this end, increased attention has been directed at how anesthetic drugs alter the functional connectivity between brain regions as defined through neuroimaging. However, the effects of anesthesia on temporal dynamics at functional network scales is less well understood. Here, we examine such dynamics in view of the free-energy principle, which postulates that brain dynamics tend to promote lower energy (more organized) states. We specifically engaged the hypothesis that such low-energy states play an important role in maintaining conscious awareness. To investigate this hypothesis, we analyzed resting-state BOLD fMRI data from human volunteers during wakefulness and under sevoflurane general anesthesia. Our approach, which extends an idea previously used in the characterization of neuron-scale populations, involves thresholding the BOLD time series and using a normalized Hamiltonian energy function derived from the Ising model. Our major finding is that the brain spends significantly more time in lower energy states during eyes-closed wakefulness than during general anesthesia. This effect is especially pronounced in networks thought to be critical for maintaining awareness, suggesting a crucial cognitive role for both the structure and the dynamical landscape of these networks. Author Summary We show that activity in the human brain, as captured by functional magnetic resonance imaging (fMRI), is more organized during wakefulness than during general anesthesia. This increased organization corresponds to a decrease in a statistical-physics-inspired energy measure among brain regions of shared functional specialization (resting-state networks) that have putative roles in conscious awareness and attention. Characterizing the energy distributions in this way reveals significant changes in the dynamics of brain activity in different states of consciousness, insights that are not observable in the average functional connectivity data alone. Our results indicate that the ability of brain networks to sustain stable representations, via their dynamics, may be crucial for consciousness and cognition.

Author Summary This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference—and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models that can entertain both discrete and continuous states. This leads to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to characterize the requisite message passing, and link this formal characterization to canonical microcircuits and extrinsic connectivity in the brain. Abstract This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference—and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models. Crucially, these models can entertain both discrete and continuous states, leading to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to elucidate the requisite message passing in terms of its form and scheduling. To accommodate mixed generative models (of discrete and continuous states), one also has to consider link nodes or factors that enable discrete and continuous representations to talk to each other. When mapping the implicit computational architecture onto neuronal connectivity, several interesting features emerge. For example, Bayesian model averaging and comparison, which link discrete and continuous states, may be implemented in thalamocortical loops. These and other considerations speak to a computational connectome that is inherently state dependent and self-organizing in ways that yield to a principled (variational) account. We conclude with simulations of reading that illustrate the implicit neuronal message passing, with a special focus on how discrete (semantic) representations inform, and are informed by, continuous (visual) sampling of the sensorium.

Functional coupling networks are widely used to characterize collective patterns of activity in neural populations. Here, we ask whether functional couplings reflect the subtle changes, such as in physiological interactions, believed to take place during learning. We infer functional network models reproducing the spiking activity of simultaneously recorded neurons in prefrontal cortex (PFC) of rats, during the performance of a cross-modal rule shift task (task epoch), and during preceding and following sleep epochs. A large-scale study of the 96 recorded sessions allows us to detect, in about 20% of sessions, effective plasticity between the sleep epochs. These coupling modifications are correlated with the coupling values in the task epoch, and are supported by a small subset of the recorded neurons, which we identify by means of an automatized procedure. These potentiated groups increase their coativation frequency in the spiking data between the two sleep epochs, and, hence, participate to putative experience-related cell assemblies. Study of the reactivation dynamics of the potentiated groups suggests a possible connection with behavioral learning. Reactivation is largely driven by hippocampal ripple events when the rule is not yet learned, and may be much more autonomous, and presumably sustained by the potentiated PFC network, when learning is consolidated. Author Summary Cell assemblies coding for memories are widely believed to emerge through synaptic modification resulting from learning, yet their identification from activity is very arduous. We propose a functional-connectivity-based approach to identify experience-related cell assemblies from multielectrode recordings in vivo, and apply it to the prefrontal cortex activity of rats recorded during a task epoch and the preceding and following sleep epochs. We infer functional couplings between the recorded cells in each epoch. Comparisons of the functional coupling networks across the epochs allow us to identify effective potentiation between the two sleep epochs. The neurons supporting these potentiated interactions strongly coactivate during the task and subsequent sleep epochs, but not in the preceding sleep, and, hence, presumably belong to an experience-related cell assembly. Study of the reactivation of this assembly in response to hippocampal ripple inputs suggests possible relations between the stage of behavorial learning and memory consolidation mechanisms.

Structural covariance examines covariation of gray matter morphology between brain regions and across individuals. Despite significant interest in the influence of age on structural covariance patterns, no study to date has provided a complete life span perspective—bridging childhood with early, middle, and late adulthood—on the development of structural covariance networks. Here, we investigate the life span trajectories of structural covariance in six canonical neurocognitive networks: default, dorsal attention, frontoparietal control, somatomotor, ventral attention, and visual. By combining data from five open-access data sources, we examine the structural covariance trajectories of these networks from 6 to 94 years of age in a sample of 1,580 participants. Using partial least squares, we show that structural covariance patterns across the life span exhibit two significant, age-dependent trends. The first trend is a stable pattern whose integrity declines over the life span. The second trend is an inverted-U that differentiates young adulthood from other age groups. Hub regions, including posterior cingulate cortex and anterior insula, appear particularly influential in the expression of this second age-dependent trend. Overall, our results suggest that structural covariance provides a reliable definition of neurocognitive networks across the life span and reveal both shared and network-specific trajectories. Author Summary The importance of life span perspectives is increasingly apparent in understanding normative interactions of large-scale neurocognitive networks. Although recent work has made significant strides in understanding the functional and structural connectivity of these networks, there has been comparatively little attention to life span trajectories of structural covariance networks. In this study we examine patterns of structural covariance across the life span for six neurocognitive networks. Our results suggest that networks exhibit both network-specific stable patterns of structural covariance as well as shared age-dependent trends. Previously identified hub regions seem to show a strong influence on the expression of these age-related trajectories. These results provide initial evidence for a multimodal understanding of structural covariance in network structure-function interaction across the life course.

Author Summary Network methods have opened new insights on structure and functional dynamics of the human brain. However, constructing functional brain networks is far from trivial—the neuroscientific community still lacks a standard definition of the nodes of brain networks. In the present article, we consider the two most commonly used approaches: using either imaging voxels or predefined Regions of Interest (ROIs) as nodes of the network. We investigate what happens when voxel-level signals are averaged for obtaining ROI-level networks. We introduce the concept of ROI consistency to characterize the similarity of the dynamics of voxels in an ROI. With the help of consistency, we show that although voxels in an ROI are assumed to behave similarly, this assumption does not hold for all ROIs. Abstract The functional network approach, where fMRI BOLD time series are mapped to networks depicting functional relationships between brain areas, has opened new insights into the function of the human brain. In this approach, the choice of network nodes is of crucial importance. One option is to consider fMRI voxels as nodes. This results in a large number of nodes, making network analysis and interpretation of results challenging. A common alternative is to use predefined clusters of anatomically close voxels, Regions of Interest (ROIs). This approach assumes that voxels within ROIs are functionally similar. Because these two approaches result in different network structures, it is crucial to understand what happens to network connectivity when moving from the voxel level to the ROI level. We show that the consistency of ROIs, defined as the mean Pearson correlation coefficient between the time series of their voxels, varies widely in resting-state experimental data. Therefore the assumption of similar voxel dynamics within each ROI does not generally hold. Further, the time series of low-consistency ROIs may be highly correlated, resulting in spurious links in ROI-level networks. Based on these results, we recommend that averaging BOLD signals over anatomically defined ROIs should be carefully considered.

Perceptual decisions vary in the speed at which we make them. Evidence suggests that translating sensory information into perceptual decisions relies on distributed interacting neural populations, with decision speed hinging on power modulations of the neural oscillations. Yet the dependence of perceptual decisions on the large-scale network organization of coupled neural oscillations has remained elusive. We measured magnetoencephalographic signals in human listeners who judged acoustic stimuli composed of carefully titrated clouds of tone sweeps. These stimuli were used in two task contexts, in which the participants judged the overall pitch or direction of the tone sweeps. We traced the large-scale network dynamics of the source-projected neural oscillations on a trial-by-trial basis using power-envelope correlations and graph-theoretical network discovery. In both tasks, faster decisions were predicted by higher segregation and lower integration of coupled beta-band (∼16–28 Hz) oscillations. We also uncovered the brain network states that promoted faster decisions in either lower-order auditory or higher-order control brain areas. Specifically, decision speed in judging the tone sweep direction critically relied on the nodal network configurations of anterior temporal, cingulate, and middle frontal cortices. Our findings suggest that global network communication during perceptual decision-making is implemented in the human brain by large-scale couplings between beta-band neural oscillations. Author Summary The speed at which we make perceptual decisions varies. This translation of sensory information into perceptual decisions hinges on dynamic changes in neural oscillatory activity. However, the large-scale neural-network embodiment supporting perceptual decision-making is unclear. We addressed this question by experimenting two auditory perceptual decision-making situations. Using graph-theoretical network discovery, we traced the large-scale network dynamics of coupled neural oscillations to uncover the brain network states that support the speed of auditory perceptual decisions. We found that higher network segregation of coupled beta-band oscillations supports faster auditory perceptual decisions over trials. Moreover, when auditory perceptual decisions are relatively difficult, the decision speed benefits from higher segregation of frontal cortical areas, but lower segregation and greater integration of auditory cortical areas.

Traumatic brain injury (TBI) affects structural connectivity, triggering the reorganization of structural–functional circuits in a manner that remains poorly understood. We focus here on brain network reorganization in relation to postural control deficits after TBI. We enrolled young participants who had suffered moderate to severe TBI, comparing them to young, typically developing control participants. TBI patients (but not controls) recruited prefrontal regions to interact with two separated networks: (1) a subcortical network, including parts of the motor network, basal ganglia, cerebellum, hippocampus, amygdala, posterior cingulate gyrus, and precuneus; and (2) a task-positive network, involving regions of the dorsal attention system, together with dorsolateral and ventrolateral prefrontal regions. We also found that the increased prefrontal connectivity in TBI patients was correlated with some postural control indices, such as the amount of body sway, whereby patients with worse balance increased their connectivity in frontal regions more strongly. The increased prefrontal connectivity found in TBI patients may provide the structural scaffolding for stronger cognitive control of certain behavioral functions, consistent with the observations that various motor tasks are performed less automatically following TBI and that more cognitive control is associated with such actions. Author Summary Using a new hierarchical atlas whose modules are relevant for both structure and function, we found increased structural and functional connectivity in prefrontal regions in TBI patients as compared to controls, in addition to a general pattern of overall decreased connectivity across the TBI brain. Although this increased prefrontal connectivity reflected interactions between brain areas when participants were at rest, the enhanced connectivity was found to be negatively correlated with active behavior such as postural control performance. Thus our findings, obtained when the brain was at rest, potentially reflect how TBI patients orchestrate task-related activations to support behavior in everyday life. In particular, our findings of enhanced connectivity in TBI might help these patients overcome deficits in cerebellar and subcortical connections, in addition to compensating for deficits when interacting with the task-positive network. Hence, it appears that greater cognitive control is exerted over certain actions in order to overcome deficits in their automatic processing.

Human intelligence has been conceptualized as a complex system of dissociable cognitive processes, yet studies investigating the neural basis of intelligence have typically emphasized the contributions of discrete brain regions or, more recently, of specific networks of functionally connected regions. Here we take a broader, systems perspective in order to investigate whether intelligence is an emergent property of synchrony within the brain’s intrinsic network architecture. Using a large sample of resting-state fMRI and cognitive data ( n = 830), we report that the synchrony of functional interactions within and across distributed brain networks reliably predicts fluid and flexible intellectual functioning. By adopting a whole-brain, systems-level approach, we were able to reliably predict individual differences in human intelligence by characterizing features of the brain’s intrinsic network architecture. These findings hold promise for the eventual development of neural markers to predict changes in intellectual function that are associated with neurodevelopment, normal aging, and brain disease. Author Summary In our study, we aimed to understand how individual differences in intellectual functioning are reflected in the intrinsic network architecture of the human brain. We applied statistical methods, known as spectral decompositions , in order to identify individual differences in the synchronous patterns of spontaneous brain activity that reliably predict core aspects of human intelligence. The synchrony of brain activity at rest across multiple discrete neural networks demonstrated positive relationships with fluid intelligence. In contrast, global synchrony within the brain’s network architecture reliably, and inversely, predicted mental flexibility, a core facet of intellectual functioning. The multinetwork systems approach described here represents a methodological and conceptual extension of earlier efforts that related differences in intellectual ability to variations in specific brain regions, networks, or their interactions. Our findings suggest that the neural basis of complex, integrative cognitive functions can be most completely understood from the perspective of network neuroscience.

Scale-free neuronal dynamics and interareal correlations are emergent characteristics of spontaneous brain activity. How such dynamics and the anatomical patterns of neuronal connectivity are mutually related in brain networks has, however, remained unclear. We addressed this relationship by quantifying the network colocalization of scale-free neuronal activity—both neuronal avalanches and long-range temporal correlations (LRTCs)—and functional connectivity (FC) by means of intracranial and noninvasive human resting-state electrophysiological recordings. We found frequency-specific colocalization of scale-free dynamics and FC so that the interareal couplings of LRTCs and the propagation of neuronal avalanches were most pronounced in the predominant pathways of FC. Several control analyses and the frequency specificity of network colocalization showed that the results were not trivial by-products of either brain dynamics or our analysis approach. Crucially, scale-free neuronal dynamics and connectivity also had colocalized modular structures at multiple levels of network organization, suggesting that modules of FC would be endowed with partially independent dynamic states. These findings thus suggest that FC and scale-free dynamics—hence, putatively, neuronal criticality as well—coemerge in a hierarchically modular structure in which the modules are characterized by dense connectivity, avalanche propagation, and shared dynamic states. Author Summary The framework of criticality has been suggested to explain the scale-free dynamics of neuronal activity in complex interaction networks. However, the in vivo relationship between scale-free dynamics and functional connectivity (FC) has remained unclear. We used human intracranial and noninvasive electrophysiological measurements to map scale-free dynamics and connectivity. We found that the propagation of fast activity avalanches and the interareal coupling of slow, long-range temporal correlations—two key forms of scale-free neuronal dynamics—were nontrivially colocalized with the strongest functional connections. Most importantly, scale-free dynamics and FC exhibited similar modular network structures. FC and scale-free dynamics, and possibly also neuronal criticality, appear to co-emerge in a modular architecture in which the modules are characterized internally by shared dynamic states, avalanche propagation, and dense functional connectivity.

Author Summary In recent years, connectomics has provided significant insights into the topological complexity of brain networks. However, the temporal complexity of brain networks still remains somewhat poorly understood. In this study we used entropy analysis to demonstrate that the properties of network segregation (the clustering coefficient) and integration (the participation coefficient) are temporally complex, situated between complete order and disorder. Our results also indicated that “segregated network nodes” may attempt to minimize the network’s entropy, whereas “integrated network nodes” require a higher information load, and therefore need to increase entropy. We believe that combining temporal information from functional brain networks and entropy can be used to test the decomplexification theory of disease, especially in neurological and psychiatric conditions characterized by paroxysmal brain abnormalities (e.g., schizophrenia and epilepsy). Abstract The brain operates in a complex way. The temporal complexity underlying macroscopic and spontaneous brain network activity is still to be understood. In this study, we explored the brain’s complexity by combining functional connectivity, graph theory, and entropy analyses in 25 healthy people using task-free functional magnetic resonance imaging. We calculated the pairwise instantaneous phase synchrony between 8,192 brain nodes for a total of 200 time points. This resulted in graphs for which time series of clustering coefficients (the “cliquiness” of a node) and participation coefficients (the between-module connectivity of a node) were estimated. For these two network metrics, sample entropy was calculated. The procedure produced a number of results: (1) Entropy is higher for the participation coefficient than for the clustering coefficient. (2) The average clustering coefficient is negatively related to its associated entropy, whereas the average participation coefficient is positively related to its associated entropy. (3) The level of entropy is network-specific to the participation coefficient, but not to the clustering coefficient. High entropy for the participation coefficient was observed in the default-mode, visual, and motor networks. These results were further validated using an independent replication dataset. Our work confirms that brain networks are temporally complex. Entropy is a good candidate metric to explore temporal network alterations in diseases with paroxysmal brain disruptions, including schizophrenia and epilepsy.

AUTHOR SUMMARY Our ability to thoughtfully engage with the world around us changes appreciably as we transition from childhood to adulthood. Yet, how our brains develop to enable that change remains far from understood. Here we used network science—traditionally applied to the study of social networks like Facebook or Twitter—and machine learning to show that growing cognitive abilities are accompanied by greater flexibility of brain regions within distributed networks. This flexibility is greatest in the executive system, which is critical for higher-order cognitive functions and increases in expression and flexibility from childhood to young adulthood. These results suggest that healthy development is facilitated by an increasing precedence of executive networks and a greater switching of the regions and interactions subserving these networks. Abstract Cognitive function evolves significantly over development, enabling flexible control of human behavior. Yet, how these functions are instantiated in spatially distributed and dynamically interacting networks, or graphs, that change in structure from childhood to adolescence is far from understood. Here we applied a novel machine-learning method to track continuously overlapping and time-varying subgraphs in the brain at rest within a sample of 200 healthy youth (ages 8–11 and 19–22) drawn from the Philadelphia Neurodevelopmental Cohort. We uncovered a set of subgraphs that capture surprisingly integrated and dynamically changing interactions among known cognitive systems. We observed that subgraphs that were highly expressed were especially transient, flexibly switching between high and low expression over time. This transience was particularly salient in a subgraph predominantly linking frontoparietal regions of the executive system, which increases in both expression and flexibility from childhood to young adulthood. Collectively, these results suggest that healthy development is accompanied by an increasing precedence of executive networks and a greater switching of the regions and interactions subserving these networks.