Related Articles

Background

Little is known about the changes of brain structural and functional connectivity networks underlying the pathophysiology in migraine. We aimed to investigate how the cortical network reorganization is altered by frequent cortical overstimulation associated with migraine.

Methodology/Principal Findings

Gray matter volumes and resting-state functional magnetic resonance imaging signal correlations were employed to construct structural and functional networks between brain regions in 43 female patients with migraine (PM) and 43 gender-matched healthy controls (HC) by using graph theory-based approaches. Compared with the HC group, the patients showed abnormal global topology in both structural and functional networks, characterized by higher mean clustering coefficients without significant change in the shortest absolute path length, which indicated that the PM lost optimal topological organization in their cortical networks. Brain hubs related to pain-processing revealed abnormal nodal centrality in both structural and functional networks, including the precentral gyrus, orbital part of the inferior frontal gyrus, parahippocampal gyrus, anterior cingulate gyrus, thalamus, temporal pole of the middle temporal gyrus and the inferior parietal gyrus. Negative correlations were found between migraine duration and regions with abnormal centrality. Furthermore, the dysfunctional connections in patients' cortical networks formed into a connected component and three dysregulated modules were identified involving pain-related information processing and motion-processing visual networks.

Conclusions

Our results may reflect brain alteration dynamics resulting from migraine and suggest that long-term and high-frequency headache attacks may cause both structural and functional connectivity network reorganization. The disrupted information exchange between brain areas in migraine may be reshaped into a hierarchical modular structure progressively.

Purpose

To determine whether neuropsychological functioning differs in breast cancer survivors six months after completion of adjuvant treatment as compared to women without cancer.

Methods

Participants were 187 women diagnosed with ductal carcinoma in situ (DCIS), Stage I, or Stage II breast cancer and 187 age- and geographic- matched women without cancer. Of survivors, 97 had been treated post-surgery with chemotherapy only or chemotherapy plus radiotherapy and 90 had been treated post-surgery with radiotherapy only.

Results

Small but statistically significant differences in cognitive functioning and cognitive impairment were observed in survivors treated with chemotherapy and their matched controls and also in survivors treated with radiotherapy only and their matched controls. No group differences were observed in cognitive complaints.

Conclusion

Data from the current study suggest that cognitive deficits are subtle and likely due to the general effects of cancer diagnosis and treatment rather than systemic treatment.

Recently, many researchers have used graph theory to study the aberrant brain structures in Alzheimer's disease (AD) and have made great progress. However, the characteristics of the cortical network in Mild Cognitive Impairment (MCI) are still largely unexplored. In this study, the gray matter volumes obtained from magnetic resonance imaging (MRI) for all brain regions except the cerebellum were parcellated into 90 areas using the automated anatomical labeling (AAL) template to construct cortical networks for 98 normal controls (NCs), 113 MCIs and 91 ADs. The measurements of the network properties were calculated for each of the three groups respectively. We found that all three cortical networks exhibited small-world properties and those strong interhemispheric correlations existed between bilaterally homologous regions. Among the three cortical networks, we found the greatest clustering coefficient and the longest absolute path length in AD, which might indicate that the organization of the cortical network was the least optimal in AD. The small-world measures of the MCI network exhibited intermediate values. This finding is logical given that MCI is considered to be the transitional stage between normal aging and AD. Out of all the between-group differences in the clustering coefficient and absolute path length, only the differences between the AD and normal control groups were statistically significant. Compared with the normal controls, the MCI and AD groups retained their hub regions in the frontal lobe but showed a loss of hub regions in the temporal lobe. In addition, altered interregional correlations were detected in the parahippocampus gyrus, medial temporal lobe, cingulum, fusiform, medial frontal lobe, and orbital frontal gyrus in groups with MCI and AD. Similar to previous studies of functional connectivity, we also revealed increased interregional correlations within the local brain lobes and disrupted long distance interregional correlations in groups with MCI and AD.

Author Summary

Understanding the progression of Alzheimer's disease (AD) is essential. We investigated networks of cortical connectivity along a continuum from normal to AD. Mild Cognitive Impairment (MCI) has been implicated as transitional between normal aging and AD. By investigating the characteristics of cortical networks in these three stages (normal, MCI and AD), we found that all three networks exhibited small-world properties. These properties indicate efficient information transfer in the human brain. We also found that the small-world measures of the MCI network were intermediate to those of the normal controls and the patients with AD. This supports the opinion that MCI is a transitional stage between normal aging and AD. Additionally, we found altered interregional correlations in patients with MCI and AD, which may indicate that a compensatory system interacts with cerebral atrophy. The presence of compensatory mechanisms in patients with MCI and AD may enable them to use additional cognitive resources to function on a more nearly normal level. In future, we need to integrate the multi-level network features obtained with various functional and anatomical brain imaging technologies on different scales to understand the pathophysiological mechanism of MCI and AD. We propose brainnetome to represent such integration framework.

Purpose of review

Recent developments in the statistical physics of complex networks have been translated to neuroimaging data in an effort to enhance our understanding of human brain structural and functional networks. This review focuses on studies using graph theoretical measures applied to structural MRI, diffusion MRI, functional MRI, electroencephalography and magnetoencephalography data.

Recent findings

Complex network properties have been identified with some consistency in all modalities of neuroimaging data and over a range of spatial and time scales. Conserved properties include small-worldness, high efficiency of information transfer for low wiring cost, modularity, and the existence of network hubs. Structural and functional network metrics have been found to be heritable and to change with normal aging. Clinical studies, principally in Alzheimer’s disease and schizophrenia, have identified abnormalities of network configuration in patients. Future work will likely involve efforts to synthesize structural and functional networks in integrated models and to explore the inter-dependence of network configuration and cognitive performance.

Summary

Graph theoretical analysis of neuroimaging data is growing rapidly and could potentially provide a relatively simple but powerful quantitative framework to describe and compare whole human brain structural and functional networks under diverse experimental and clinical conditions.

During development, the healthy human brain constructs a host of large-scale, distributed, function-critical neural networks. Neurodegenerative diseases have been thought to target these systems, but this hypothesis has not been systematically tested in living humans. We used network-sensitive neuroimaging methods to show that five different neurodegenerative syndromes cause circumscribed atrophy within five distinct healthy human intrinsic functional connectivity networks. We further discovered a direct link between intrinsic connectivity and gray matter structure. Across healthy individuals, nodes within each functional network exhibited tightly correlated gray matter volumes. The findings suggest that human neural networks can be defined by synchronous baseline activity, a unified corticotrophic fate, and selective vulnerability to neurodegenerative illness. Future studies may clarify how these complex systems are assembled during development and undermined by disease.

Background

To understand neurophysiological mechanisms underlying cognitive dysfunction in low-grade glioma (LGG) patients by evaluating the spatial structure of 'resting-state' brain networks with graph theory.

Methods

Standardized tests measuring 6 neurocognitive domains were administered in 17 LGG patients and 17 healthy controls. Magnetoencephalography (MEG) recordings were conducted during eyes-closed 'resting state'. The phase lag index (PLI) was computed in seven frequency bands to assess functional connectivity between brain areas. Spatial patterns were characterized with graph theoretical measures such as clustering coefficient (local connectivity), path length (global integration), network small world-ness (ratio of clustering coefficient/path length) and degree correlation (the extent to which connected nodes have similar degrees).

Results

Compared to healthy controls, patients performed poorer on psychomotor functioning, attention, information processing, and working memory. Patients displayed higher short- and long-distance synchronization and clustering coefficient in the theta band, whereas a lower clustering coefficient and small world-ness were observed in the beta band. A lower degree correlation was found in the upper gamma band. LGG patients with higher clustering coefficient, longer path length, and lower degree correlations in delta and lower alpha band were characterized by poorer neurocognitive performance.

Conclusion

LGG patients display higher short- and long-distance synchronization within the theta band. Network analysis revealed changes (in particularly the theta, beta, and upper gamma band) suggesting disturbed network architecture. Moreover, correlations between network characteristics and neurocognitive performance were found, Widespread changes in the strength and spatial organization of brain networks may be responsible for cognitive dysfunction in glioma patients.

The complex organization of connectivity in the human brain is incompletely understood. Recently, topological measures based on graph theory have provided a new approach to quantify large-scale cortical networks. These methods have been applied to anatomical connectivity data on non-human species and cortical networks have been shown to have small-world topology, associated with high local and global efficiency of information transfer. Anatomical networks derived from cortical thickness measurements have shown the same organizational properties of the healthy human brain, consistent with similar results reported in functional networks derived from resting state functional MRI and MEG data. Here we show, using anatomical networks derived from analysis of inter-regional covariation of gray matter volume in magnetic resonance imaging (MRI) data on 259 healthy volunteers, that classical divisions of cortex (multimodal, unimodal and transmodal) have some distinct topological attributes. While all cortical divisions shared non-random properties of small-worldness and efficient wiring (short mean Euclidean distance between connected regions), the multimodal network had a hierarchical organization, dominated by frontal hubs with low clustering, whereas the transmodal network was assortative. Moreover, in a sample of 203 people with schizophrenia, multimodal network organization was abnormal, as indicated by reduced hierarchy, the loss of frontal and the emergence of non-frontal hubs, and increased connection distance. We propose that the topological differences between divisions of normal cortex may represent the outcome of different growth processes for multimodal and transmodal networks; and that neurodevelopmental abnormalities in schizophrenia specifically impact multimodal cortical organization.

Aging is associated with reorganization of brain in both structure and function. In recent years, graph theoretical analysis of brain organization has drawn increasing attention, and reorganization of brain in aging has been investigated in terms of connectivity and networks in topology such as modular organization, global and local efficiency, and small-worldness. Beyond studying on abnormity in local brain regions, connectivity quantifies alternations of correlation between two regions that may be spatially far separated, and graph theoretical analysis of brain network examines the complex interactions among multiple regions. This article reviewed complex brain networks of human in normal aging or with age-related diseases such as stroke and Alzheimer’s disease after a technical introduction of brain networks and graph theoretical analysis. We further discussed the relationship between the functional and the structural brain networks of subjects in aging or with age-related diseases. Finally, we proposed several interesting topics for future research in this field.

The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons). A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron “giant component” of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been “rewired” to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.

Purpose

Adjuvant chemotherapy has been associated with mild cognitive decline among a subset of breast cancer survivors. Late cognitive effects after chemotherapy can have a deleterious impact on survivor quality of life and functional health; however, the etiology of chemotherapy-related cognitive dysfunction remains unknown.

Patients and Methods

We present a case of monozygotic twins who are discordant for breast cancer and chemotherapy exposure (ie, one twin contracted breast cancer and underwent chemotherapy, and the other had no breast cancer). As part of a larger study, each was evaluated with standardized, self-report measures of cognitive function, standard neuropsychological tests, and structural and functional magnetic resonance imaging (MRI).

Results

Results indicated small differences in neuropsychological test performance but striking contrasts in self-reported cognitive complaints and structural and functional MRI images. Specifically, the twin who underwent chemotherapy had substantially more subjective cognitive complaints, more white matter hyperintensities on MRI, and an expanded spatial extent of brain activation during working memory processing than her nonaffected twin.

Conclusion

This case illustrates possible physiologic mechanisms that could produce long-term cognitive complaints among chemotherapy recipients and help formulate hypotheses for further empirical study in the area of chemotherapy-associated cognitive dysfunction.

Voxel-based morphometry was used to compare brain structure morphology of survivors of posterior fossa brain tumor (PFBT) with that of normal sibling controls to investigate disease- or cancer treatment–induced changes. Two different spatial normalization approaches that are available in public domain software (free-form deformation (FFD) and discrete cosine transform (DCT)) were compared for accuracy of normalization in the PFBT patients. Anatomical landmark matching demonstrated that spatial normalization was more accurate with FFD than with DCT. Voxel-based morphometry of the FFD-normalized magnetic resonance images from PFBT survivors and sibling controls detected reduced gray matter density in the thalamus and entorhinal cortex and reduced white matter density in the internal capsule, hypothalamus, corpus callosum, and cuneus of the occipital lobe in the PFBT survivors. Identification of these morphologic lesions may help localize the neural substrates of disease- or therapy-induced cognitive deficits in survivors of childhood cancer.

Recent applications of network theory to brain networks as well as the expanding empirical databases of brain architecture spawn an interest in novel techniques for analyzing connectivity patterns in the brain. Treating individual brain structures as nodes in a directed graph model permits the application of graph theoretical concepts to the analysis of these structures within their large-scale connectivity networks. In this paper, we explore the application of concepts from graph and game theory toward this end. Specifically, we utilize the Shapley value principle, which assigns a rank to players in a coalition based upon their individual contributions to the collective profit of that coalition, to assess the contributions of individual brain structures to the graph derived from the global connectivity network. We report Shapley values for variations of a prefrontal network, as well as for a visual cortical network, which had both been extensively investigated previously. This analysis highlights particular nodes as strong or weak contributors to global connectivity. To understand the nature of their contribution, we compare the Shapley values obtained from these networks and appropriate controls to other previously described nodal measures of structural connectivity. We find a strong correlation between Shapley values and both betweenness centrality and connection density. Moreover, a stepwise multiple linear regression analysis indicates that approximately 79% of the variance in Shapley values obtained from random networks can be explained by betweenness centrality alone. Finally, we investigate the effects of local lesions on the Shapley ratings, showing that the present networks have an immense structural resistance to degradation. We discuss our results highlighting the use of such measures for characterizing the organization and functional role of brain networks.

The characterization of the topological architecture of complex networks underlying the structural and functional organization of the brain is a basic challenge in neuroscience. However, direct evidence for anatomical connectivity networks in the human brain remains scarce. Here, we utilized diffusion tensor imaging deterministic tractography to construct a macroscale anatomical network capturing the underlying common connectivity pattern of human cerebral cortex in a large sample of subjects (80 young adults) and further quantitatively analyzed its topological properties with graph theoretical approaches. The cerebral cortex was divided into 78 cortical regions, each representing a network node, and 2 cortical regions were considered connected if the probability of fiber connections exceeded a statistical criterion. The topological parameters of the established cortical network (binarized) resemble that of a “small-world” architecture characterized by an exponentially truncated power-law distribution. These characteristics imply high resilience to localized damage. Furthermore, this cortical network was characterized by major hub regions in association cortices that were connected by bridge connections following long-range white matter pathways. Our results are compatible with previous structural and functional brain networks studies and provide insight into the organizational principles of human brain anatomical networks that underlie functional states.

We investigated the large-scale functional cortical connectivity network in focal hand dystonia (FHD) patients using graph theoretic measures to assess efficiency. High-resolution EEGs were recorded in 15 FHD patients and 15 healthy volunteers at rest and during a simple sequential finger tapping task. Mutual information (MI) values of wavelet coefficients were estimated to create an association matrix between EEG electrodes, and to produce a series of adjacency matrices or graphs, G, by thresholding with network cost. Efficiency measures of small-world networks were assessed. As a result, we found that FHD patients have economical small-world properties in their brain functional networks in the alpha and beta bands. During a motor task, in the beta band network, FHD patients have decreased efficiency of small-world networks, whereas healthy volunteers increase efficiency. Reduced efficient beta band network in FHD patients during the task was consistently observed in global efficiency, cost-efficiency, and maximum cost-efficiency. This suggests that the beta band functional cortical network of FHD patients is reorganized even during a task that does not induce dystonic symptoms, representing a loss of long-range communication and abnormal functional integration in large-scale brain functional cortical networks. Moreover, negative correlations between efficiency measures and duration of disease were found, indicating that the longer duration of disease, the less efficient the beta band network in FHD patients. In regional efficiency analysis, FHD patients at rest have high regional efficiency at supplementary motor cortex (SMA) compared with healthy volunteers; however, it is diminished during the motor task, possibly reflecting abnormal inhibition in FHD patients. The present study provides the first evidence with graph theory for abnormal reconfiguration of brain functional networks in FHD during motor task.

Many real-world phenomena have been described in terms of large networks. Networks have been invaluable models for the understanding of biological systems. Since proteins carry out most biological processes, we focus on analysing protein–protein interaction (PPI) networks. Proteins interact to perform a function. Thus, PPI networks reflect the interconnected nature of biological processes and analysing their structural properties could provide insights into biological function and disease. We have already demonstrated, by using a sensitive graph theoretic method for comparing topologies of node neighbourhoods called ‘graphlet degree signatures’, that proteins with similar surroundings in PPI networks tend to perform the same functions. Here, we explore whether the involvement of genes in cancer suggests the similarity of their topological ‘signatures’ as well. By applying a series of clustering methods to proteins' topological signature similarities, we demonstrate that the obtained clusters are significantly enriched with cancer genes. We apply this methodology to identify novel cancer gene candidates, validating 80 per cent of our predictions in the literature. We also validate predictions biologically by identifying cancer-related negative regulators of melanogenesis identified in our siRNA screen. This is encouraging, since we have done this solely from PPI network topology. We provide clear evidence that PPI network structure around cancer genes is different from the structure around non-cancer genes. Understanding the underlying principles of this phenomenon is an open question, with a potential for increasing our understanding of complex diseases.

Background

The neurobiological underpinnings of bipolar disorder are not well understood. Previous neuroimaging findings have been inconsistent; however, new methods for three-dimensional (3-D) computational image analysis may better characterize neuroanatomic changes than standard volumetric measures.

Methods

We used high-resolution magnetic resonance imaging and cortical pattern matching methods to map gray matter differences in 28 adults with bipolar disorder, 70% of whom were lithium-treated (mean age = 36.1 ± 10.5; 13 female subject), and 28 healthy control subjects (mean age = 35.9 ± 8.5; 11 female subjects). Detailed spatial analyses of gray matter density (GMD) were conducted by measuring local proportions of gray matter at thousands of homologous cortical locations.

Results

Gray matter density was significantly greater in bipolar patients relative to control subjects in diffuse cortical regions. Greatest differences were found in bilateral cingulate and paralimbic cortices, brain regions critical for attentional, motivational, and emotional modulation. Secondary region of interest (ROI) analyses indicated significantly greater GMD in the right anterior cingulate among lithium-treated bipolar patients (n = 20) relative to those not taking lithium (n = 8).

Conclusions

These brain maps are consistent with previous voxel-based morphometry reports of greater GMD in portions of the anterior limbic network in bipolar patients and suggest neurotrophic effects of lithium as a possible etiology of these neuroanatomic differences.

Modern non-invasive brain imaging technologies, such as diffusion weighted magnetic resonance imaging (DWI), enable the mapping of neural fiber tracts in the white matter, providing a basis to reconstruct a detailed map of brain structural connectivity networks. Brain connectivity networks differ from random networks in their topology, which can be measured using small worldness, modularity, and high-degree nodes (hubs). Still, little is known about how individual differences in structural brain network properties relate to age, sex, or genetic differences. Recently, some groups have reported brain network biomarkers that enable differentiation among individuals, pairs of individuals, and groups of individuals. In addition to studying new topological features, here we provide a unifying general method to investigate topological brain networks and connectivity differences between individuals, pairs of individuals, and groups of individuals at several levels of the data hierarchy, while appropriately controlling false discovery rate (FDR) errors. We apply our new method to a large dataset of high quality brain connectivity networks obtained from High Angular Resolution Diffusion Imaging (HARDI) tractography in 303 young adult twins, siblings, and unrelated people. Our proposed approach can accurately classify brain connectivity networks based on sex (93% accuracy) and kinship (88.5% accuracy). We find statistically significant differences associated with sex and kinship both in the brain connectivity networks and in derived topological metrics, such as the clustering coefficient and the communicability matrix.

Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence) of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution.

Objective

To investigate the topological alterations of the whole-brain white-matter (WM) structural networks in patients with neuromyelitis optica (NMO).

Methods

The present study involved 26 NMO patients and 26 age- and sex-matched healthy controls. WM structural connectivity in each participant was imaged with diffusion-weighted MRI and represented in terms of a connectivity matrix using deterministic tractography method. Graph theory-based analyses were then performed for the characterization of brain network properties. A multiple linear regression analysis was performed on each network metric between the NMO and control groups.

Results

The NMO patients exhibited abnormal small-world network properties, as indicated by increased normalized characteristic path length, increased normalized clustering and increased small-worldness. Furthermore, largely similar hub distributions of the WM structural networks were observed between NMO patients and healthy controls. However, regional efficiency in several brain areas of NMO patients was significantly reduced, which were mainly distributed in the default-mode, sensorimotor and visual systems. Furthermore, we have observed increased regional efficiency in a few brain regions such as the orbital parts of the superior and middle frontal and fusiform gyri.

Conclusion

Although the NMO patients in this study had no discernible white matter T2 lesions in the brain, we hypothesize that the disrupted topological organization of WM networks provides additional evidence for subtle, widespread cerebral WM pathology in NMO.

Community structure is a universal and significant feature of many complex networks in biology, society, and economics. Community structure has also been revealed in human brain structural and functional networks in previous studies. However, communities overlap and share many edges and nodes. Uncovering the overlapping community structure of complex networks remains largely unknown in human brain networks. Here, using regional gray matter volume, we investigated the structural brain network among 90 brain regions (according to a predefined anatomical atlas) in 462 young, healthy individuals. Overlapped nodes between communities were defined by assuming that nodes (brain regions) can belong to more than one community. We demonstrated that 90 brain regions were organized into 5 overlapping communities associated with several well-known brain systems, such as the auditory/language, visuospatial, emotion, decision-making, social, control of action, memory/learning, and visual systems. The overlapped nodes were mostly involved in an inferior-posterior pattern and were primarily related to auditory and visual perception. The overlapped nodes were mainly attributed to brain regions with higher node degrees and nodal efficiency and played a pivotal role in the flow of informa- tion through the structural brain network. Our results revealed fuzzy boundaries between communities by identifying overlapped nodes and provided new insights into the understanding of the relationship between the structure and function of the human brain. This study provides the first report of the overlapping community structure of the structural network of the human brain.

Small-world networks are a class of networks that exhibit efficient long-distance communication and tightly interconnected local neighborhoods. In recent years, functional and structural brain networks have been examined using network theory-based methods, and consistently shown to have small-world properties. Moreover, some voxel-based brain networks exhibited properties of scale-free networks, a class of networks with mega-hubs. However, there are considerable inconsistencies across studies in the methods used and the results observed, particularly between region-based and voxel-based brain networks. We constructed functional brain networks at multiple resolutions using the same resting-state fMRI data, and compared various network metrics, degree distribution, and localization of nodes of interest. It was found that the networks with higher resolutions exhibited the properties of small-world networks more prominently. It was also found that voxel-based networks were more robust against network fragmentation compared to region-based networks. Although the degree distributions of all networks followed an exponentially truncated power law rather than true power law, the higher the resolution, the closer the distribution was to a power law. The voxel-based analyses also enhanced visualization of the results in the 3D brain space. It was found that nodes with high connectivity tended have high efficiency, a co-localization of properties that was not as consistently observed in the region-based networks. Our results demonstrate benefits of constructing the brain network at the finest scale the experiment will permit.

In recent years, graph theoretical analyses of neuroimaging data have increased our understanding of the organization of large-scale structural and functional brain networks. However, tools for pipeline application of graph theory for analyzing topology of brain networks is still lacking. In this report, we describe the development of a graph-analysis toolbox (GAT) that facilitates analysis and comparison of structural and functional network brain networks. GAT provides a graphical user interface (GUI) that facilitates construction and analysis of brain networks, comparison of regional and global topological properties between networks, analysis of network hub and modules, and analysis of resilience of the networks to random failure and targeted attacks. Area under a curve (AUC) and functional data analyses (FDA), in conjunction with permutation testing, is employed for testing the differences in network topologies; analyses that are less sensitive to the thresholding process. We demonstrated the capabilities of GAT by investigating the differences in the organization of regional gray-matter correlation networks in survivors of acute lymphoblastic leukemia (ALL) and healthy matched Controls (CON). The results revealed an alteration in small-world characteristics of the brain networks in the ALL survivors; an observation that confirm our hypothesis suggesting widespread neurobiological injury in ALL survivors. Along with demonstration of the capabilities of the GAT, this is the first report of altered large-scale structural brain networks in ALL survivors.

Recently, it has been demonstrated that several complex systems may have simple graph-theoretic characterizations as so-called ‘small-world’ and ‘scale-free’ networks. These networks have also been applied to the gross neural connectivity between primate cortical areas and the nervous system of Caenorhabditis elegans. Here, we extend this work to a specific neural circuit of the vertebrate brain—the medial reticular formation (RF) of the brainstem—and, in doing so, we have made three key contributions. First, this work constitutes the first model (and quantitative review) of this important brain structure for over three decades. Second, we have developed the first graph-theoretic analysis of vertebrate brain connectivity at the neural network level. Third, we propose simple metrics to quantitatively assess the extent to which the networks studied are small-world or scale-free. We conclude that the medial RF is configured to create small-world (implying coherent rapid-processing capabilities), but not scale-free, type networks under assumptions which are amenable to quantitative measurement.

Abnormalities in the topology of brain networks may be an important feature and etiological factor for psychogenic non-epileptic seizures (PNES). To explore this possibility, we applied a graph theoretical approach to functional networks based on resting state EEGs from 13 PNES patients and 13 age- and gender-matched controls. The networks were extracted from Laplacian-transformed time-series by a cross-correlation method. PNES patients showed close to normal local and global connectivity and small-world structure, estimated with clustering coefficient, modularity, global efficiency, and small-worldness (SW) metrics, respectively. Yet the number of PNES attacks per month correlated with a weakness of local connectedness and a skewed balance between local and global connectedness quantified with SW, all in EEG alpha band. In beta band, patients demonstrated above-normal resiliency, measured with assortativity coefficient, which also correlated with the frequency of PNES attacks. This interictal EEG phenotype may help improve differentiation between PNES and epilepsy. The results also suggest that local connectivity could be a target for therapeutic interventions in PNES. Selective modulation (strengthening) of local connectivity might improve the skewed balance between local and global connectivity and so prevent PNES events.

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e.g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a “fingerprint”. Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the “uncertainty” of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.