The human functional brain network demonstrates structural and dynamical resilience to targeted attack

Exploring the link between brain topological resilience and cognitive performance in the context of aging and vascular risk factors: A cross-ethnicity population-based study

Brain aging is typically associated with a significant decline in cognitive performance. Vascular risk factors (VRF) and subsequent atherosclerosis (AS) play a major role in this process. Brain resilience reflects the brain's ability to withstand external perturbations, but the relationship of brain resilience with cognition during the aging process remains unclear. Here, we investigated how brain topological resilience (BTR) is associated with cognitive performance in the face of aging and vascular risk factors. We used data from two cross-ethnicity community cohorts, PolyvasculaR Evaluation for Cognitive Impairment and Vascular Events (PRECISE, n = 2220) and Sydney Memory and Ageing Study (MAS, n = 246). We conducted an attack simulation on brain structural networks based on k-shell decomposition and node degree centrality. BTR was defined based on changes in the size of the largest subgroup of the network during the simulation process. Subsequently, we explored the negative correlations of BTR with age, VRF, and AS, and its positive correlation with cognitive performance. Furthermore, using structural equation modeling (SEM), we constructed path models to analyze the directional dependencies among these variables, demonstrating that aging, AS, and VRF affect cognition by disrupting BTR. Our results also indicated the specificity of this metric, independent of brain volume. Overall, these findings underscore the supportive role of BTR on cognition during aging and highlight its potential application as an imaging marker for objective assessment of brain cognitive performance.

Pathologic Substrates of Structural Brain Network Resilience and Topology in Parkinson Disease Decedents

BACKGROUND AND OBJECTIVES

In Parkinson disease (PD), α-synuclein spreading through connected brain regions leads to neuronal loss and brain network disruptions. With diffusion-weighted imaging (DWI), it is possible to capture conventional measures of brain network organization and more advanced measures of brain network resilience. We aimed to investigate which neuropathologic processes contribute to regional network topologic changes and brain network resilience in PD.

METHODS

Using a combined postmortem MRI and histopathology approach, PD and control brain donors with available postmortem in situ 3D T1-weighted MRI, DWI, and brain tissue were selected from the Netherlands Brain Bank and Normal Aging Brain Collection Amsterdam. Probabilistic tractography was performed, and conventional network topologic measures of regional eigenvector centrality and clustering coefficient, and brain network resilience (change in global efficiency upon regional node failure) were calculated. PSer129 α-synuclein, phosphorylated-tau, β-amyloid, neurofilament light-chain immunoreactivity, and synaptophysin density were quantified in 8 cortical regions. Group differences and correlations were assessed with rank-based nonparametric tests, with age, sex, and postmortem delay as covariates.

RESULTS

Nineteen clinically defined and pathology-confirmed PD (7 F/12 M, 81 ± 7 years) and 15 control (8 F/7 M, 73 ± 9 years) donors were included. With regional conventional measures, we found lower eigenvector centrality only in the parahippocampal gyrus in PD (d = -1.08, 95% CI 0.003-0.010, p = 0.021), which did not associate with underlying pathology. No differences were found in regional clustering coefficient. With the more advanced measure of brain network resilience, we found that the PD brain network was less resilient to node failure of the dorsal anterior insula compared with the control brain network (d = -1.00, 95% CI 0.0012-0.0015, p = 0.018). This change was not directly driven by neuropathologic processes within the dorsal anterior insula or in connected regions but was associated with higher Braak α-synuclein staging (rs = -0.40, p = 0.036).

DISCUSSION

Although our cohort might suffer from selection bias, our results highlight that regional network disturbances are more complex to interpret than previously believed. Regional neuropathologic processes did not drive regional topologic changes, but a global increase in α-synuclein pathology had a widespread effect on brain network reorganization in PD.

EEG functional connectivity after perinatal stroke

Impaired cognitive functioning after perinatal stroke has been associated with long-term functional brain network changes. We explored brain functional connectivity using a 64-channel resting-state electroencephalogram in 12 participants, aged 5-14 years with a history of unilateral perinatal arterial ischemic or haemorrhagic stroke. A control group of 16 neurologically healthy subjects was also included-each test subject was compared with multiple control subjects, matched by sex and age. Functional connectomes from the alpha frequency band were calculated for each subject and the differences in network graph metrics between the 2 groups were analyzed. Our results suggest that the functional brain networks of children with perinatal stroke show evidence of disruption even years after the insult and that the scale of changes appears to be influenced by the lesion volume. The networks remain more segregated and show a higher synchronization at both whole-brain and intrahemispheric level. Total interhemispheric strength was higher in children with perinatal stroke compared with healthy controls.

Accumulation of network redundancy marks the early stage of Alzheimer's disease

Brain wiring redundancy counteracts aging-related cognitive decline by reserving additional communication channels as a neuroprotective mechanism. Such a mechanism plays a potentially important role in maintaining cognitive function during the early stages of neurodegenerative disorders such as Alzheimer's disease (AD). AD is characterized by severe cognitive decline and involves a long prodromal stage of mild cognitive impairment (MCI). Since MCI subjects are at high risk of converting to AD, identifying MCI individuals is essential for early intervention. To delineate the redundancy profile during AD progression and enable better MCI diagnosis, we define a metric that reflects redundant disjoint connections between brain regions and extract redundancy features in three high-order brain networks-medial frontal, frontoparietal, and default mode networks-based on dynamic functional connectivity (dFC) captured by resting-state functional magnetic resonance imaging (rs-fMRI). We show that redundancy increases significantly from normal control (NC) to MCI individuals and decreases slightly from MCI to AD individuals. We further demonstrate that statistical features of redundancy are highly discriminative and yield state-of-the-art accuracy of up to 96.8 ± 1.0% in support vector machine (SVM) classification between NC and MCI individuals. This study provides evidence supporting the notion that redundancy serves as a crucial neuroprotective mechanism in MCI.

Early path dominance as a principle for neurodevelopment

We perform targeted attack, a systematic computational unlinking of the network, to analyze its effects on global communication across the brain network through its giant cluster. Across diffusion magnetic resonance images from individuals in the UK Biobank, Adolescent Brain Cognitive Development Study and Developing Human Connectome Project, we find that targeted attack procedures on increasing white matter tract lengths and densities are remarkably invariant to aging and disease. Time-reversing the attack computation suggests a mechanism for how brains develop, for which we derive an analytical equation using percolation theory. Based on a close match between theory and experiment, our results demonstrate that tracts are limited to emanate from regions already in the giant cluster and tracts that appear earliest in neurodevelopment are those that become the longest and densest.

Network analysis reveals abnormal functional brain circuitry in anxious dogs

Anxiety is a common disease within human psychiatric disorders and has also been described as a frequently neuropsychiatric problem in dogs. Human neuroimaging studies showed abnormal functional brain networks might be involved in anxiety. In this study, we expected similar changes in network topology are also present in dogs. We performed resting-state functional MRI on 25 healthy dogs and 13 patients. The generic Canine Behavioral Assessment & Research Questionnaire was used to evaluate anxiety symptoms. We constructed functional brain networks and used graph theory to compare the differences between two groups. No significant differences in global network topology were found. However, focusing on the anxiety circuit, global efficiency and local efficiency were significantly higher, and characteristic path length was significantly lower in the amygdala in patients. We detected higher connectivity between amygdala-hippocampus, amygdala-mesencephalon, amygdala-thalamus, frontal lobe-hippocampus, frontal lobe-thalamus, and hippocampus-thalamus, all part of the anxiety circuit. Moreover, correlations between network metrics and anxiety symptoms were significant. Altered network measures in the amygdala were correlated with stranger-directed fear and excitability; altered degree in the hippocampus was related to attachment/attention seeking, trainability, and touch sensitivity; abnormal frontal lobe function was related to chasing and familiar dog aggression; attachment/attention seeking was correlated with functional connectivity between amygdala-hippocampus and amygdala-thalamus; familiar dog aggression was related to global network topology change. These findings may shed light on the aberrant topological organization of functional brain networks underlying anxiety in dogs.

Dynamic and Functional Alterations of Neuronal Networks In Vitro upon Physical Damage: A Proof of Concept

There is a growing technological interest in combining biological neuronal networks with electronic ones, specifically for biological computation, human-machine interfacing and robotic implants. A major challenge for the development of these technologies is the resilience of the biological networks to physical damage, for instance, when used in harsh environments. To tackle this question, here, we investigated the dynamic and functional alterations of rodent cortical networks grown in vitro that were physically damaged, either by sequentially removing groups of neurons that were central for information flow or by applying an incision that cut the network in half. In both cases, we observed a remarkable capacity of the neuronal cultures to cope with damage, maintaining their activity and even reestablishing lost communication pathways. We also observed-particularly for the cultures cut in half-that a reservoir of healthy neurons surrounding the damaged region could boost resilience by providing stimulation and a communication bridge across disconnected areas. Our results show the remarkable capacity of neuronal cultures to sustain and recover from damage, and may be inspirational for the development of future hybrid biological-electronic systems.

Characterization of structural and functional network organization after focal prefrontal lesions in humans in proof of principle study

Lesion research classically maps behavioral effects of focal damage to the directly injured brain region. However, such damage can also have distant effects that can be assessed with modern imaging methods. Furthermore, the combination and comparison of imaging methods in a lesion model may shed light on the biological basis of structural and functional networks in the healthy brain. We characterized network organization assessed with multiple MRI imaging modalities in 13 patients with chronic focal damage affecting either superior or inferior frontal gyrus (SFG, IFG) and 18 demographically matched healthy Controls. We first defined structural and functional network parameters in Controls and then investigated grey matter (GM) and white matter (WM) differences between patients and Controls. Finally, we examined the differences in functional coupling to large-scale resting state networks (RSNs). The results suggest lesions are associated with widespread within-network GM loss at distal sites, yet leave WM and RSNs relatively preserved. Lesions to either prefrontal region also had a similar relative level of impact on structural and functional networks. The findings provide initial evidence for causal contributions of specific prefrontal regions to brain networks in humans that will ultimately help to refine models of the human brain.

Percolation may explain efficiency, robustness, and economy of the brain

The brain consists of billions of neurons connected by ultra-dense synapses, showing remarkable efficiency, robust flexibility, and economy in information processing. It is generally believed that these advantageous properties are rooted in brain connectivity; however, direct evidence remains absent owing to technical limitations or theoretical vacancy. This research explores the origins of these properties in the largest yet brain connectome of the fruit fly. We reveal that functional connectivity formation in the brain can be explained by a percolation process controlled by synaptic excitation-inhibition (E/I) balance. By increasing the E/I balance gradually, we discover the emergence of these properties as byproducts of percolation transition when the E/I balance arrives at 3:7. As the E/I balance keeps increase, an optimal E/I balance 1:1 is unveiled to ensure these three properties simultaneously, consistent with previous in vitro experimental predictions. Once the E/I balance reaches over 3:2, an intrinsic limitation of these properties determined by static (anatomical) brain connectivity can be observed. Our work demonstrates that percolation, a universal characterization of critical phenomena and phase transitions, may serve as a window toward understanding the emergence of various brain properties.

Brain Network Alterations in Rectal Cancer Survivors With Depression Tendency: Evaluation With Multimodal Magnetic Resonance Imaging

Surgery and chemotherapy may increase depression tendency in patients with rectal cancer (RC). Nevertheless, few comprehensive studies are conducted on alterations of brain network induced by depression tendency in patients with RC. Resting-state functional magnetic resonance imaging (rs-fMRI) and diffusion tensor imaging (DTI) data were collected from 42 patients with RC with surgery and chemotherapy and 38 healthy controls (HCs). Functional network (FN) was constructed from extracting average time courses in brain regions, and structural network (SN) was established by deterministic tractography. Graph theoretical analysis was used to calculate network properties. Networks resilient of two networks were assessed. Clinical correlation analysis was explored between altered network parameters and Hamilton depression scale (HAMD) score. This study revealed impaired FN and SN at both local and global levels and changed nodal efficiency and abnormal small-worldness property in patients with RC. On the whole, all FNs are more robust than SN. Moreover, compared with HC, patients with RC show less robustness in both networks. Regions with decreased nodal efficiency were associated with HAMD score. These cognitive dysfunctions are mainly attributable to depression-related brain functional and structural network alterations. Brain network reorganization is to prevent patients with RC from more serious depression after surgery and chemotherapy.

Simulated Attack Reveals How Lesions Affect Network Properties in Poststroke Aphasia

Aphasia is a prevalent cognitive syndrome caused by stroke. The rarity of premorbid imaging and heterogeneity of lesion obscures the links between the local effects of the lesion, global anatomic network organization, and aphasia symptoms. We applied a simulated attack approach in humans to examine the effects of 39 stroke lesions (16 females) on anatomic network topology by simulating their effects in a control sample of 36 healthy (15 females) brain networks. We focused on measures of global network organization thought to support overall brain function and resilience in the whole brain and within the left hemisphere. After removing lesion volume from the network topology measures and behavioral scores [the Western Aphasia Battery Aphasia Quotient (WAB-AQ), four behavioral factor scores obtained from a neuropsychological battery, and a factor sum], we compared the behavioral variance accounted for by simulated poststroke connectomes to that observed in the randomly permuted data. Global measures of anatomic network topology in the whole brain and left hemisphere accounted for 10% variance or more of the WAB-AQ and the lexical factor score beyond lesion volume and null permutations. Streamline networks provided more reliable point estimates than FA networks. Edge weights and network efficiency were weighted most highly in predicting the WAB-AQ for FA networks. Overall, our results suggest that global network measures provide modest statistical value beyond lesion volume when predicting overall aphasia severity, but less value in predicting specific behaviors. Variability in estimates could be induced by premorbid ability, deafferentation and diaschisis, and neuroplasticity following stroke.SIGNIFICANCE STATEMENT Poststroke, the remaining neuroanatomy maintains cognition and supports recovery. However, studies often use small, cross-sectional samples that cannot fully model the interactions between lesions and other variables that affect networks in stroke. Alternate methods are required to account for these effects. "Simulated attack" models are computational approaches that apply virtual damage to the brain and measure their putative consequences. Using a simulated attack model, we estimated how simulated damage to anatomic networks could account for language performance. Overall, our results reveal that global network measures can provide modest statistical value predicting overall aphasia severity, but less value in predicting specific behaviors. These findings suggest that more theoretically precise network models could be necessary to robustly predict individual outcomes in aphasia.

Preparing for a Second Attack: A Lesion Simulation Study on Network Resilience After Stroke

Background:

Does the brain become more resilient after a first stroke to reduce the consequences of a new lesion? Although recurrent strokes are a major clinical issue, whether and how the brain prepares for a second attack is unknown. This is due to the difficulties to obtain an appropriate dataset of stroke patients with comparable lesions, imaged at the same interval after onset. Furthermore, timing of the recurrent event remains unpredictable.

Methods:

Here, we used a novel clinical lesion simulation approach to test the hypothesis that resilience in brain networks increases during stroke recovery. Sixteen highly selected patients with a lesion restricted to the primary motor cortex were recruited. At 3 time points of the index event (10 days, 3 weeks, 3 months), we mimicked recurrent infarcts by deletion of nodes in brain networks (resting-state functional magnetic resonance imaging). Graph measures were applied to determine resilience (global efficiency after attack) and wiring cost (mean degree) of the network.

Results:

At 10 days and 3 weeks after stroke, resilience was similar in patients and controls. However, at 3 months, although motor function had fully recovered, resilience to clinically representative simulated lesions was higher compared to controls (cortical lesion P =0.012; subcortical: P =0.009; cortico-subcortical: P =0.009). Similar results were found after random ( P =0.012) and targeted ( P =0.015) attacks.

Conclusions:

Our results suggest that, in this highly selected cohort of patients with lesions restricted to the primary motor cortex, brain networks reconfigure to increase resilience to future insults. Lesion simulation is an innovative approach, which may have major implications for stroke therapy. Individualized neuromodulation strategies could be developed to foster resilient network reconfigurations after a first stroke to limit the consequences of future attacks.

Disrupted Control Architecture of Brain Network in Disorder of Consciousness

The human brain controls various cognitive functions via the functional coordination of multiple brain regions in an efficient and robust way. However, the relationship between consciousness state and the control mode of brain networks is poorly explored. Using multi-channel EEG, the present study aimed to characterize the abnormal control architecture of functional brain networks in the patients with disorders of consciousness (DOC). Resting state EEG data were collected from 40 DOC patients with different consciousness levels and 24 healthy subjects. Functional brain networks were constructed in five different EEG frequency bands and the broadband in the source level. Subsequently, a control architecture framework based on the minimum dominating set was applied to investigate the of control mode of functional brain networks for the subjects with different conscious states. Results showed that regardless of the consciousness levels, the functional networks of human brain operate in a distributed and overlapping control architecture different from that of random networks. Compared to the healthy controls, the patients have a higher control cost manifested by more minimum dominating nodes and increased degree of distributed control, especially in the alpha band. The ability to withstand network attack for the control architecture is positive correlated with the consciousness levels. The distributed of control increased correlation levels with Coma Recovery Scale-Revised score and improved separation between unresponsive wakefulness syndrome and minimal consciousness state. These findings may benefit our understanding of consciousness and provide potential biomarkers for the assessment of consciousness levels.

Excitatory-Inhibitory Homeostasis and Diaschisis: Tying the Local and Global Scales in the Post-stroke Cortex

Maintaining a balance between excitatory and inhibitory activity is an essential feature of neural networks of the neocortex. In the face of perturbations in the levels of excitation to cortical neurons, synapses adjust to maintain excitatory-inhibitory (EI) balance. In this review, we summarize research on this EI homeostasis in the neocortex, using stroke as our case study, and in particular the loss of excitation to distant cortical regions after focal lesions. Widespread changes following a localized lesion, a phenomenon known as diaschisis, are not only related to excitability, but also observed with respect to functional connectivity. Here, we highlight the main findings regarding the evolution of excitability and functional cortical networks during the process of post-stroke recovery, and how both are related to functional recovery. We show that cortical reorganization at a global scale can be explained from the perspective of EI homeostasis. Indeed, recovery of functional networks is paralleled by increases in excitability across the cortex. These adaptive changes likely result from plasticity mechanisms such as synaptic scaling and are linked to EI homeostasis, providing a possible target for future therapeutic strategies in the process of rehabilitation. In addition, we address the difficulty of simultaneously studying these multiscale processes by presenting recent advances in large-scale modeling of the human cortex in the contexts of stroke and EI homeostasis, suggesting computational modeling as a powerful tool to tie the meso- and macro-scale processes of recovery in stroke patients.

Alterations of dynamic redundancy of functional brain subnetworks in Alzheimer's disease and major depression disorders

The human brain is not only efficiently but also "redundantly" connected. The redundancy design could help the brain maintain resilience to disease attacks. This paper explores subnetwork-level redundancy dynamics and the potential of such metrics in disease studies. As such, we looked into specific functional subnetworks, including those associated with high-level functions. We investigated how the subnetwork redundancy dynamics change along with Alzheimer's disease (AD) progression and with major depressive disorder (MDD), two major disorders that could share similar subnetwork alterations. We found an increased dynamic redundancy of the subcortical-cerebellum subnetwork and its connections to other high-order subnetworks in the mild cognitive impairment (MCI) and AD compared to the normal control (NC). With gained spatial specificity, we found such a redundancy index was sensitive to disease symptoms and could act as a protective mechanism to prevent the collapse of the brain network and functions. The dynamic redundancy of the medial frontal subnetwork and its connections to the frontoparietal subnetwork was also found decreased in MDD compared to NC. The spatial specificity of the redundancy dynamics changes may provide essential knowledge for a better understanding of shared neural substrates in AD and MDD.

Topographical functional correlates of interindividual differences in executive functions in young healthy twins

Executive functions (EF) are a set of higher-order cognitive abilities that enable goal-directed behavior by controlling lower-level operations. In the brain, those functions have been traditionally associated with activity in the Frontoparietal Network, but recent neuroimaging studies have challenged this view in favor of more widespread cortical involvement. In the present study, we aimed to explore whether the network that serves as critical hubs at rest, which we term network reliance, differentiate individuals as a function of their level of EF. Furthermore, we investigated whether such differences are driven by genetic as compared to environmental factors. For this purpose, resting-state functional magnetic resonance imaging data and the behavioral testing of 453 twins from the Colorado Longitudinal Twins Study were analyzed. Separate indices of EF performance were obtained according to a bifactor unity/diversity model, distinguishing between three independent components representing: Common EF, Shifting-specific and Updating-specific abilities. Through an approach of step-wise in silico network lesioning of the individual functional connectome, we show that interindividual differences in EF are associated with different dependencies on neural networks at rest. Furthermore, these patterns show evidence of mild heritability. Such findings add knowledge to the understanding of brain states at rest and their connection with human behavior, and how they might be shaped by genetic influences.

Frontoparietal network resilience is associated with protection against cognitive decline in Parkinson's disease

Though Parkinson's disease is primarily defined as a movement disorder, it is also characterized by a range of non-motor symptoms, including cognitive decline. The onset and progression of cognitive decline in individuals with Parkinson's disease is variable, and the neurobiological mechanisms that contribute to, or protect against, cognitive decline in Parkinson's disease are poorly understood. Using resting-state functional magnetic resonance imaging data collected from individuals with Parkinson's disease with and without cognitive decline, we examined the relationship between topological brain-network resilience and cognition in Parkinson's disease. By leveraging network attack analyses, we demonstrate that relative to individuals with Parkinson's disease experiencing cognitive decline, the frontoparietal network in cognitively stable individuals with Parkinson's disease is significantly more resilient to network perturbation. Our findings suggest that the topological robustness of the frontoparietal network is associated with the absence of cognitive decline in individuals with Parkinson's disease.

Heritability of brain resilience to perturbation in humans

Resilience is the capacity of complex systems to persist in the face of external perturbations and retain their functional properties and performance. In the present study, we investigated how individual variations in brain resilience, which might influence response to stress, aging and disease, are influenced by genetics and/or the environment, with potential implications for the implementation of resilience-boosting interventions. Resilience estimates were derived from in silico lesioning of either brain regions or functional connections constituting the connectome of healthy individuals belonging to two different large and unique datasets of twins, specifically: 463 individual twins from the Human Connectome Project and 453 individual twins from the Colorado Longitudinal Twin Study. As has been reported previously, moderate heritability was found for several topological indexes of brain efficiency and modularity. Importantly, evidence of heritability was found for resilience measures based on removal of brain connections rather than specific single regions, suggesting that genetic influences on resilience are preferentially directed toward region-to-region communication rather than local brain activity. Specifically, the strongest genetic influence was observed for moderately weak, long-range connections between a specific subset of functional brain networks: the Default Mode, Visual and Sensorimotor networks. These findings may help identify a link between brain resilience and network-level alterations observed in neurological and psychiatric diseases, as well as inform future studies investigating brain shielding interventions against physiological and pathological perturbations.

A Feature Tensor-Based Epileptic Detection Model Based on Improved Edge Removal Approach for Directed Brain Networks

Electroencephalograph (EEG) plays a significant role in the diagnostics process of epilepsy, but the detection rate is unsatisfactory when the length of interictal EEG signals is relatively short. Although the deliberate attacking theories for undirected brain network based on node removal method can extract potential network features, the node removal method fails to sufficiently consider the directionality of brain electrical activities. To solve the problems above, this study proposes a feature tensor-based epileptic detection method of directed brain networks. First, a directed functional brain network is constructed by calculating the transfer entropy of EEG signals between different electrodes. Second, the edge removal method is used to imitate the disruptions of brain connectivity, which may be related to the disorder of brain diseases, to obtain a sequence of residual networks. After that, topological features of these residual networks are extracted based on graph theory for constructing a five-way feature tensor. To exploit the inherent interactions among multiple modes of the feature tensor, this study uses the Tucker decomposition method to get a core tensor which is finally reshaped into a vector and input into the support vectors machine (SVM) classifier. Experiment results suggest that the proposed method has better epileptic screening performance for short-term interictal EEG data.

Seven Properties of Self-Organization in the Human Brain

The principle of self-organization has acquired a fundamental significance in the newly emerging field of computational philosophy. Self-organizing systems have been described in various domains in science and philosophy including physics, neuroscience, biology and medicine, ecology, and sociology. While system architecture and their general purpose may depend on domain-specific concepts and definitions, there are (at least) seven key properties of self-organization clearly identified in brain systems: (1) modular connectivity, (2) unsupervised learning, (3) adaptive ability, (4) functional resiliency, (5) functional plasticity, (6) from-local-to-global functional organization, and (7) dynamic system growth. These are defined here in the light of insight from neurobiology, cognitive neuroscience and Adaptive Resonance Theory (ART), and physics to show that self-organization achieves stability and functional plasticity while minimizing structural system complexity. A specific example informed by empirical research is discussed to illustrate how modularity, adaptive learning, and dynamic network growth enable stable yet plastic somatosensory representation for human grip force control. Implications for the design of “strong” artificial intelligence in robotics are brought forward.

Tumor grade-related language and control network reorganization in patients with left cerebral glioma

Language processing relies on both a functionally specialized language network and a domain-general cognitive control network. Yet, how the two networks reorganize after damage resulting from diffuse and progressive glioma remains largely unknown. To address this issue, 130 patients with left cerebral gliomas, including 77 patients with low-grade glioma (LGG, WHO grade Ⅰ/II), 53 patients with high-grade glioma (HGG, WHO grade III/IV) and 38 healthy controls (HC) were adopted. The changes in resting-state functional connectivity (rsFC) of the language network and the cingulo-opercular/fronto-parietal (CO-FP) network were examined using network-based statistics. We found that tumor grade negatively correlated with language scores and language network integrity. Compared with HCs, patients with LGGs exhibited slight language deficits, both decreased and increased changes in rsFC of language network, and nearly normal CO-FP network. Patients with HGGs had significantly lower language scores than those with LGG and exhibited more severe language and CO-FP network disruptions than HCs or patients with LGGs. Moreover, we found that in patients with HGGs, the decreased rsFCs of language network were positively correlated with language scores. Together, our findings suggest tumor grade-related network reorganization of both language and control networks underlie the different levels of language impairments observed in patients with gliomas.

Impact of targeted attack on the spontaneous activity in spatial and biologically-inspired neuronal networks

We study the structural and dynamical consequences of damage in spatial neuronal networks. Inspired by real in vitro networks, we construct directed networks embedded in a two-dimensional space and follow biological rules for designing the wiring of the system. As a result, synthetic cultures display strong metric correlations similar to those observed in real experiments. In its turn, neuronal dynamics is incorporated through the Izhikevich model adopting the parameters derived from observation in real cultures. We consider two scenarios for damage, targeted attacks on those neurons with the highest out-degree and random failures. By analyzing the evolution of both the giant connected component and the dynamical patterns of the neurons as nodes are removed, we observe that network activity halts for a removal of 50% of the nodes in targeted attacks, much lower than the 70% node removal required in the case of random failures. Notably, the decrease of neuronal activity is not gradual. Both damage scenarios portray "boosts" of activity just before full silencing that are not present in equivalent random (Erdös-Rényi) graphs. These boosts correspond to small, spatially compact subnetworks that are able to maintain high levels of activity. Since these subnetworks are absent in the equivalent random graphs, we hypothesize that metric correlations facilitate the existence of local circuits sufficiently integrated to maintain activity, shaping an intrinsic mechanism for resilience.

Brain functional connectivity correlates of coping styles

Coping abilities represent the individual set of mental and behavioral strategies adopted when facing stress or traumatic experiences. Coping styles related to avoidance have been linked to a disposition to develop psychiatric disorders such as PTSD, anxiety, and major depression, whereas problem-oriented coping skills have been positively correlated with well-being and high quality of life. Even though coping styles constitute an important determinant of resilience and can impact many aspects of everyday living, no study has investigated their brain functional connectivity underpinnings in humans. Here we analyzed both psychometric scores of coping and resting-state fMRI data from 102 healthy adult participants. Controlling for personality and problem-solving abilities, we identified significant links between the propensity to adopt different coping styles and the functional connectivity profiles of regions belonging to the default mode (DMN) and anterior salience (AS) networks-namely, the anterior cingulate cortex, left frontopolar cortex, and left angular gyrus. Also, a reduced negative correlation between AS and DMN nodes explained variability in one specific coping style, related to avoiding problems while focusing on the emotional component of the stressor at hand, instead of relying on cognitive resources. These results might be integrated with current neurophysiological models of resilience and individual responses to stress, in order to understand the propensity to develop clinical conditions (e.g., PTSD) and predict the outcomes of psychotherapeutic interventions.

Reconstructing missing complex networks against adversarial interventions

Interactions within complex network components define their operational modes, collective behaviors and global functionality. Understanding the role of these interactions is limited by either sensing methodologies or intentional adversarial efforts that sabotage the network structure. To overcome the partial observability and infer with good fidelity the unobserved network structures (latent subnetworks that are not random samples of the full network), we propose a general causal inference framework for reconstructing network structures under unknown adversarial interventions. We explore its applicability in both biological and social systems to recover the latent structures of human protein complex interactions and brain connectomes, as well as to infer the camouflaged social network structure in a simulated removal process. The demonstrated effectiveness establishes its good potential for capturing hidden information in much broader research domains.

Electroencephalography Functional Networks Reveal Global Effects of Methylphenidate in Youth with Attention Deficit/Hyperactivity Disorder

Methylphenidate (MPH) is the leading drug for treatment of attention deficit/hyperactivity disorder (ADHD), yet its underlying neuronal mechanisms are still unclear. Here, we use a dynamical brain networks approach to explore the effects of cognitive effort and MPH on ADHD subjects. Electroencephalography data were recorded from 19 ADHD subjects and 18 controls during a Go/No-Go Task. ADHD subjects completed the task twice a day over 2 days. The second session was administered post-ingestion of placebo/MPH (alternately). Controls performed two tasks in 1 day. The data were divided into 300 ms windows from -300 pre-stimulus until 1200 ms post-stimulus. Brain networks were constructed per subject and window, from which network metrics were extracted and compared across the experimental conditions. We identified an immediate shift of global connectivity and of network segregation after the stimulus for both groups, followed by a gradual return to baseline. Decreased global connectivity was found to be 400-700 ms post-stimulus in ADHD compared with controls, and it was normalized post-MPH. An increase of the networks' segregation occurred post-placebo at 100-400 and 400-700 ms post-stimulus, yet it was inhibited post-MPH. These global alterations resulted mainly from changes in task-relevant frontal and parietal regions. The networks of medicated ADHD subjects and controls exhibited a more significant and lasting change, relative to baseline, compared with those of nonmedicated ADHD. These results suggest impaired network flexibility in ADHD, corrected by MPH.

Impaired Efficiency and Resilience of Structural Network in Spinocerebellar Ataxia Type 3

Background: Recent studies have shown that the patients with spinocerebellar ataxia type 3 (SCA3) may not only have disease involvement in the cerebellum and brainstem but also in the cerebral regions. However, the relations between the widespread degenerated brain regions remains incompletely explored. Methods: In the present study, we investigate the topological properties of the brain networks of SCA3 patients (n = 40) constructed based on the correlation of three-dimensional fractal dimension values. Random and targeted attacks were applied to measure the network resilience of normal and SCA3 groups. Results: The SCA3 networks had significantly smaller clustering coefficients (P < 0.05) and global efficiency (P < 0.05) but larger characteristic path length (P < 0.05) than the normal controls networks, implying loss of small-world features. Furthermore, the SCA3 patients were associated with reduced nodal betweenness (P < 0.001) in the left supplementary motor area, bilateral paracentral lobules, and right thalamus, indicating that the motor control circuit might be compromised. Conclusions: The SCA3 networks were more vulnerable to targeted attacks than the normal controls networks because of the effects of pathological topological organization. The SCA3 revealed a more sparsity and disrupted structural network with decreased values in the largest component size, mean degree, mean density, clustering coefficient, and global efficiency and increased value in characteristic path length. The cortico-cerebral circuits in SCA3 were disrupted and segregated into occipital-parietal (visual-spatial cognition) and frontal-pre-frontal (motor control) clusters. The cerebellum of SCA3 were segregated from cerebellum-temporal-frontal circuits and clustered into a frontal-temporal cluster (cognitive control). Therefore, the disrupted structural network presented in this study might reflect the clinical characteristics of SCA3.

Modeling driver cells in developing neuronal networks

Spontaneous emergence of synchronized population activity is a characteristic feature of developing brain circuits. Recent experiments in the developing neo-cortex showed the existence of driver cells able to impact the synchronization dynamics when single-handedly stimulated. We have developed a spiking network model capable to reproduce the experimental results, thus identifying two classes of driver cells: functional hubs and low functionally connected (LC) neurons. The functional hubs arranged in a clique orchestrated the synchronization build-up, while the LC drivers were lately or not at all recruited in the synchronization process. Notwithstanding, they were able to alter the network state when stimulated by modifying the temporal activation of the functional clique or even its composition. LC drivers can lead either to higher population synchrony or even to the arrest of population dynamics, upon stimulation. Noticeably, some LC driver can display both effects depending on the received stimulus. We show that in the model the presence of inhibitory neurons together with the assumption that younger cells are more excitable and less connected is crucial for the emergence of LC drivers. These results provide a further understanding of the structural-functional mechanisms underlying synchronized firings in developing circuits possibly related to the coordinated activity of cell assemblies in the adult brain.

Finding influential nodes for integration in brain networks using optimal percolation theory

Global integration of information in the brain results from complex interactions of segregated brain networks. Identifying the most influential neuronal populations that efficiently bind these networks is a fundamental problem of systems neuroscience. Here, we apply optimal percolation theory and pharmacogenetic interventions in vivo to predict and subsequently target nodes that are essential for global integration of a memory network in rodents. The theory predicts that integration in the memory network is mediated by a set of low-degree nodes located in the nucleus accumbens. This result is confirmed with pharmacogenetic inactivation of the nucleus accumbens, which eliminates the formation of the memory network, while inactivations of other brain areas leave the network intact. Thus, optimal percolation theory predicts essential nodes in brain networks. This could be used to identify targets of interventions to modulate brain function.

Remodeling Functional Connectivity in Multiple Sclerosis: A Challenging Therapeutic Approach

Neurons in the central nervous system are organized in functional units interconnected to form complex networks. Acute and chronic brain damage disrupts brain connectivity producing neurological signs and/or symptoms. In several neurological diseases, particularly in Multiple Sclerosis (MS), structural imaging studies cannot always demonstrate a clear association between lesion site and clinical disability, originating the "clinico-radiological paradox." The discrepancy between structural damage and disability can be explained by a complex network perspective. Both brain networks architecture and synaptic plasticity may play important roles in modulating brain networks efficiency after brain damage. In particular, long-term potentiation (LTP) may occur in surviving neurons to compensate network disconnection. In MS, inflammatory cytokines dramatically interfere with synaptic transmission and plasticity. Importantly, in addition to acute and chronic structural damage, inflammation could contribute to reduce brain networks efficiency in MS leading to worse clinical recovery after a relapse and worse disease progression. These evidence suggest that removing inflammation should represent the main therapeutic target in MS; moreover, as synaptic plasticity is particularly altered by inflammation, specific strategies aimed at promoting LTP mechanisms could be effective for enhancing clinical recovery. Modulation of plasticity with different non-invasive brain stimulation (NIBS) techniques has been used to promote recovery of MS symptoms. Better knowledge of features inducing brain disconnection in MS is crucial to design specific strategies to promote recovery and use NIBS with an increasingly tailored approach.

An Evolutionary Game Theory Model of Spontaneous Brain Functioning

Our brain is a complex system of interconnected regions spontaneously organized into distinct networks. The integration of information between and within these networks is a continuous process that can be observed even when the brain is at rest, i.e. not engaged in any particular task. Moreover, such spontaneous dynamics show predictive value over individual cognitive profile and constitute a potential marker in neurological and psychiatric conditions, making its understanding of fundamental importance in modern neuroscience. Here we present a theoretical and mathematical model based on an extension of evolutionary game theory on networks (EGN), able to capture brain's interregional dynamics by balancing emulative and non-emulative attitudes among brain regions. This results in the net behavior of nodes composing resting-state networks identified using functional magnetic resonance imaging (fMRI), determining their moment-to-moment level of activation and inhibition as expressed by positive and negative shifts in BOLD fMRI signal. By spontaneously generating low-frequency oscillatory behaviors, the EGN model is able to mimic functional connectivity dynamics, approximate fMRI time series on the basis of initial subset of available data, as well as simulate the impact of network lesions and provide evidence of compensation mechanisms across networks. Results suggest evolutionary game theory on networks as a new potential framework for the understanding of human brain network dynamics.

Accounting for the complex hierarchical topology of EEG phase-based functional connectivity in network binarisation

Research into binary network analysis of brain function faces a methodological challenge in selecting an appropriate threshold to binarise edge weights. For EEG phase-based functional connectivity, we test the hypothesis that such binarisation should take into account the complex hierarchical structure found in functional connectivity. We explore the density range suitable for such structure and provide a comparison of state-of-the-art binarisation techniques, the recently proposed Cluster-Span Threshold (CST), minimum spanning trees, efficiency-cost optimisation and union of shortest path graphs, with arbitrary proportional thresholds and weighted networks. We test these techniques on weighted complex hierarchy models by contrasting model realisations with small parametric differences. We also test the robustness of these techniques to random and targeted topological attacks. We find that the CST performs consistenty well in state-of-the-art modelling of EEG network topology, robustness to topological network attacks, and in three real datasets, agreeing with our hypothesis of hierarchical complexity. This provides interesting new evidence into the relevance of considering a large number of edges in EEG functional connectivity research to provide informational density in the topology.

The Rhesus Monkey Connectome Predicts Disrupted Functional Networks Resulting from Pharmacogenetic Inactivation of the Amygdala

Contemporary research suggests that the mammalian brain is a complex system, implying that damage to even a single functional area could have widespread consequences across the system. To test this hypothesis, we pharmacogenetically inactivated the rhesus monkey amygdala, a subcortical region with distributed and well-defined cortical connectivity. We then examined the impact of that perturbation on global network organization using resting-state functional connectivity MRI. Amygdala inactivation disrupted amygdalocortical communication and distributed corticocortical coupling across multiple functional brain systems. Altered coupling was explained using a graph-based analysis of experimentally established structural connectivity to simulate disconnection of the amygdala. Communication capacity via monosynaptic and polysynaptic pathways, in aggregate, largely accounted for the correlational structure of endogenous brain activity and many of the non-local changes that resulted from amygdala inactivation. These results highlight the structural basis of distributed neural activity and suggest a strategy for linking focal neuropathology to remote neurophysiological changes.

A Powerful DREADD: Revealing Structural Drivers of Functional Dynamics

In this issue of Neuron, Grayson et al. (2016) report how inhibition of amygdala impacts amygdalocortical and corticocortical functional connectivity. Their study predicts changes in functional brain topology, induced by pharmacologic modulation of neuroanatomical circuits using designer receptors exclusively activated by designer drugs (DREADDs), through virtual lesioning of amygdala in structural brain networks.

Tired and misconnected: A breakdown of brain modularity following sleep deprivation

Sleep deprivation (SD) critically affects a range of cognitive and affective functions, typically assessed during task performance. Whether such impairments stem from changes to the brain's intrinsic functional connectivity remain largely unknown. To examine this hypothesis, we applied graph theoretical analysis on resting-state fMRI data derived from 18 healthy participants, acquired during both sleep-rested and sleep-deprived states. We hypothesized that parameters indicative of graph connectivity, such as modularity, will be impaired by sleep deprivation and that these changes will correlate with behavioral outcomes elicited by sleep loss. As expected, our findings point to a profound reduction in network modularity without sleep, evident in the limbic, default-mode, salience and executive modules. These changes were further associated with behavioral impairments elicited by SD: a decrease in salience module density was associated with worse task performance, an increase in limbic module density was predictive of stronger amygdala activation in a subsequent emotional-distraction task and a shift in frontal hub lateralization (from left to right) was associated with increased negative mood. Altogether, these results portray a loss of functional segregation within the brain and a shift towards a more random-like network without sleep, already detected in the spontaneous activity of the sleep-deprived brain. Hum Brain Mapp 38:3300-3314, 2017. © 2017 Wiley Periodicals, Inc.

Advances in the Neuroscience of Intelligence: from Brain Connectivity to Brain Perturbation

Our view is that intelligence, as expression of the complexity of the human brain and of its evolutionary path, represents an intriguing example of "system level brain plasticity": tangible proofs of this assertion lie in the strong links intelligence has with vital brain capacities as information processing (i.e., pure, rough capacity to transfer information in an efficient way), resilience (i.e., the ability to cope with loss of efficiency and/or loss of physical elements in a network) and adaptability (i.e., being able to efficiently rearrange its dynamics in response to environmental demands). Current evidence supporting this view move from theoretical models correlating intelligence and individual response to systematic "lesions" of brain connectivity, as well as from the field of Noninvasive Brain Stimulation (NiBS). Perturbation-based approaches based on techniques as transcranial magnetic stimulation (TMS) and transcranial alternating current stimulation (tACS), are opening new in vivo scenarios which could allow to disclose more causal relationship between intelligence and brain plasticity, overcoming the limitations of brain-behavior correlational evidence.

Which Brain Regions are Important for Seizure Dynamics in Epileptic Networks? Influence of Link Identification and EEG Recording Montage on Node Centralities

Nodes in large-scale epileptic networks that are crucial for seizure facilitation and termination can be regarded as potential targets for individualized focal therapies. Graph-theoretical approaches based on centrality concepts can help to identify such important nodes, however, they may be influenced by the way networks are derived from empirical data. Here we investigate evolving functional epileptic brain networks during 82 focal seizures with different anatomical onset locations that we derive from multichannel intracranial electroencephalographic recordings from 51 patients. We demonstrate how the various methodological steps (from the recording montage via node and link inference to the assessment of node centralities) affect importance estimation and discuss their impact on the interpretability of findings in the context of pathophysiological aspects of seizure dynamics.

The segregated connectome of late-life depression: a combined cortical thickness and structural covariance analysis

Late-life depression (LLD) has been associated with both generalized and focal neuroanatomical changes including gray matter atrophy and white matter abnormalities. However, previous literature has not been consistent and, in particular, its impact on the topology organization of brain networks remains to be established. In this multimodal study, we first examined cortical thickness, and applied graph theory to investigate structural covariance networks in LLD. Thirty-three subjects with LLD and 25 controls underwent T1-weighted, fluid-attenuated inversion recovery and clinical assessments. Freesurfer was used to perform vertex-wise comparisons of cortical thickness, whereas the Graph Analysis Toolbox (GAT) was implemented to construct and analyze the structural covariance networks. LLD showed a trend of lower thickness in the left insular region (p < 0.001 uncorrected). In addition, the structural network of LLD was characterized by greater segregation, particularly showing higher transitivity (i.e., measure of clustering) and modularity (i.e., tendency for a network to be organized into subnetworks). It was also less robust against random failure and targeted attacks. Despite relative cortical preservation, the topology of the LLD network showed significant changes particularly in segregation. These findings demonstrate the potential for graph theoretical approaches to complement conventional structural imaging analyses and provide novel insights into the heterogeneous etiology and pathogenesis of LLD.

Brain networks under attack: robustness properties and the impact of lesions

A growing number of studies approach the brain as a complex network, the so-called 'connectome'. Adopting this framework, we examine what types or extent of damage the brain can withstand-referred to as network 'robustness'-and conversely, which kind of distortions can be expected after brain lesions. To this end, we review computational lesion studies and empirical studies investigating network alterations in brain tumour, stroke and traumatic brain injury patients. Common to these three types of focal injury is that there is no unequivocal relationship between the anatomical lesion site and its topological characteristics within the brain network. Furthermore, large-scale network effects of these focal lesions are compared to those of a widely studied multifocal neurodegenerative disorder, Alzheimer's disease, in which central parts of the connectome are preferentially affected. Results indicate that human brain networks are remarkably resilient to different types of lesions, compared to other types of complex networks such as random or scale-free networks. However, lesion effects have been found to depend critically on the topological position of the lesion. In particular, damage to network hub regions-and especially those connecting different subnetworks-was found to cause the largest disturbances in network organization. Regardless of lesion location, evidence from empirical and computational lesion studies shows that lesions cause significant alterations in global network topology. The direction of these changes though remains to be elucidated. Encouragingly, both empirical and modelling studies have indicated that after focal damage, the connectome carries the potential to recover at least to some extent, with normalization of graph metrics being related to improved behavioural and cognitive functioning. To conclude, we highlight possible clinical implications of these findings, point out several methodological limitations that pertain to the study of brain diseases adopting a network approach, and provide suggestions for future research.

Normalization of network connectivity in hemispatial neglect recovery

OBJECTIVE

We recently reported that spatial and nonspatial attention deficits in stroke patients with hemispatial neglect are correlated at 2 weeks postonset with widespread alterations of interhemispheric and intrahemispheric functional connectivity (FC) measured with resting-state functional magnetic resonance imaging across multiple brain networks. The mechanisms underlying neglect recovery are largely unknown. In this study, we test the hypothesis that recovery of hemispatial neglect correlates with a return of network connectivity toward a normal pattern, herein defined as "network normalization."

METHODS

We measured attention deficits with a neuropsychological battery and FC in a large cohort of stroke patients at, on average, 2 weeks (n = 99), 3 months (n = 77), and 12 months (n = 64) postonset. The relationship between behavioral improvement and changes in FC was analyzed both in terms of a priori regions and networks known to be abnormal subacutely and in a data-driven manner.

RESULTS

Attention deficit recovery was mostly complete by 3 months and was significantly correlated with a normalization of abnormal FC across many networks. Improvement of attention deficits, independent of initial severity, was correlated with improvements of previously depressed interhemispheric FC across attention, sensory, and motor networks, and a restoration of the normal anticorrelation between dorsal attention/motor regions and default-mode/frontoparietal regions, particularly in the damaged hemisphere.

INTERPRETATION

These results demonstrate that abnormal network connectivity in hemispatial neglect is behaviorally relevant. A return toward normal network interactions, and presumably optimal information processing, is therefore a systems-level mechanism that is associated with improvements of attention over time after focal injury. Ann Neurol 2016;80:127-141.

Functional properties of resting state networks in healthy full-term newborns

Objective, early, and non-invasive assessment of brain function in high-risk newborns is critical to initiate timely interventions and to minimize long-term neurodevelopmental disabilities. A prerequisite to identifying deviations from normal, however, is the availability of baseline measures of brain function derived from healthy, full-term newborns. Recent advances in functional MRI combined with graph theoretic techniques may provide important, currently unavailable, quantitative markers of normal neurodevelopment. In the current study, we describe important properties of resting state networks in 60 healthy, full-term, unsedated newborns. The neonate brain exhibited an efficient and economical small world topology: densely connected nearby regions, sparse, but well integrated, distant connections, a small world index greater than 1, and global/local efficiency greater than network cost. These networks showed a heavy-tailed degree distribution, suggesting the presence of regions that are more richly connected to others (‘hubs’). These hubs, identified using degree and betweenness centrality measures, show a more mature hub organization than previously reported. Targeted attacks on hubs show that neonate networks are more resilient than simulated scale-free networks. Networks fragmented faster and global efficiency decreased faster when betweenness, as opposed to degree, hubs were attacked suggesting a more influential role of betweenness hub in the neonate network.

Brain network alterations and vulnerability to simulated neurodegeneration in breast cancer

Breast cancer and its treatments are associated with mild cognitive impairment and brain changes that could indicate an altered or accelerated brain aging process. We applied diffusion tensor imaging and graph theory to measure white matter organization and connectivity in 34 breast cancer survivors compared with 36 matched healthy female controls. We also investigated how brain networks (connectomes) in each group responded to simulated neurodegeneration based on network attack analysis. Compared with controls, the breast cancer group demonstrated significantly lower fractional anisotropy, altered small-world connectome properties, lower brain network tolerance to systematic region (node), and connection (edge) attacks and significant cognitive impairment. Lower tolerance to network attack was associated with cognitive impairment in the breast cancer group. These findings provide further evidence of diffuse white matter pathology after breast cancer and extend the literature in this area with unique data demonstrating increased vulnerability of the post-breast cancer brain network to future neurodegenerative processes.

The smarter, the stronger: intelligence level correlates with brain resilience to systematic insults

Neuroimaging evidences posit human intelligence as tightly coupled with several structural and functional brain properties, also suggesting its potential protective role against aging and neurodegenerative conditions. However, whether higher order cognition might in fact lead to a more resilient brain has not been quantitatively demonstrated yet. Here we document a relationship between individual intelligence quotient (IQ) and brain resilience to targeted and random attacks, as measured through resting-state fMRI graph-theoretical analysis in 102 healthy individuals. In this modeling context, enhanced brain robustness to targeted attacks (TA) in individuals with higher IQ is supported by an increased distributed processing capacity despite the systematic loss of the most important node(s) of the system. Moreover, brain resilience in individuals with higher IQ is supported by a set of neocortical regions mainly belonging to language and memory processing network(s), whereas regions related to emotional processing are mostly responsible for lower IQ individuals. Results suggest intelligence level among the predictors of post-lesional or neurodegenerative recovery, also promoting the evolutionary role of higher order cognition, and simultaneously suggesting a new framework for brain stimulation interventions aimed at counteract brain deterioration over time.

Weighted brain networks in disease: centrality and entropy in human immunodeficiency virus and aging

Graph theory models can produce simple, biologically informative metrics of the topology of resting-state functional connectivity (FC) networks. However, typical graph theory approaches model FC relationships between regions (nodes) as unweighted edges, complicating their interpretability in studies of disease or aging. We extended existing techniques and constructed fully connected weighted graphs for groups of age-matched human immunodeficiency virus (HIV) positive (n = 67) and HIV negative (n = 77) individuals. We compared test-retest reliability of weighted versus unweighted metrics in an independent study of healthy individuals (n = 22) and found weighted measures to be more stable. We quantified 2 measures of node centrality (closeness centrality and eigenvector centrality) to capture the relative importance of individual nodes. We also quantified 1 measure of graph entropy (diversity) to measure the variability in connection strength (edge weights) at each node. HIV was primarily associated with differences in measures of centrality, and age was primarily associated with differences in diversity. HIV and age were associated with divergent measures when evaluated at the whole graph level, within individual functional networks, and at the level of individual nodes. Graph models may allow us to distinguish previously indistinguishable effects related to HIV and age on FC.