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Applications of graph comparison in network neuroscience. A-Comparison between structural and functional brain networks. B-Tracking the dynamic of brain networks during time. C-Comparison between two groups of brain networks for two different conditions.
Source publication
Graph theoretical approach has proved an effective tool to understand, characterize, and quantify the complex brain network. However, much less attention has been paid to methods that quantitatively compare two graphs, a crucial issue in the context of brain networks. Comparing brain networks is indeed mandatory in several network neuroscience appl...
Citations
... In the biological domain, network comparison can be used to analyze which protein interactions may have equivalent functions [13]. In neuroscience, the comparison of brain networks contributes to understanding the functional differences between normal and pathological brains [14]. ...
Analyzing and characterizing the differences between networks is a fundamental and challenging problem in network science. Most previous network comparison methods that rely on topological properties have been restricted to measuring differences between two undirected networks. However, many networks, such as biological networks, social networks, and transportation networks, exhibit inherent directionality and higher-order attributes that should not be ignored when comparing networks. Therefore, we propose a motif-based directed network comparison method that captures local, global, and higher-order differences between two directed networks. Specifically, we first construct a motif distribution vector for each node, which captures the information of a node’s involvement in different directed motifs. Then, the dissimilarity between two directed networks is defined on the basis of a matrix, which is composed of the motif distribution vector of every node and the Jensen–Shannon divergence. The performance of our method is evaluated via the comparison of six real directed networks with their null models, as well as their perturbed networks based on edge perturbation. Our method is superior to the state-of-the-art baselines and is robust with different parameter settings.
... Although the VIS and VES groups exhibited comparable power distributions across all frequencies, the VIS group showed slightly lower α band activity (8)(9)(10)(11)(12) in the frontal and parietal lobes during the feedback session compared to that in the pre-feedback session. Additionally, both groups showed an increase in the α-band activity in the temporal regions and a decrease in the β-band activity (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30). The most obvious difference between the two groups was observed in the occipital lobe, where the VES group exhibited higher α band activity in both sessions. ...
... In the nodewise analysis, graph metrics are calculated for each node in a graph, and the resulting metric values for each node are compared between the graphs. This type of analysis offers several advantages, such as the ability to examine a wider range of graph features, access more data to compare different conditions, and identify specific brain regions where differences between conditions occur, rather than simply determining whether differences exist 25 . ...
The use of neurofeedback is an important aspect of effective motor rehabilitation as it offers real-time sensory information to promote neuroplasticity. However, there is still limited knowledge about how the brain’s functional networks reorganize in response to such feedback. To address this gap, this study investigates the reorganization of the brain network during motor imagery tasks when subject to visual stimulation or visual-electrotactile stimulation feedback. This study can provide healthcare professionals with a deeper understanding of the changes in the brain network and help develop successful treatment approaches for brain–computer interface-based motor rehabilitation applications. We examine individual edges, nodes, and the entire network, and use the minimum spanning tree algorithm to construct a brain network representation using a functional connectivity matrix. Furthermore, graph analysis is used to detect significant features in the brain network that might arise in response to the feedback. Additionally, we investigate the power distribution of brain activation patterns using power spectral analysis and evaluate the motor imagery performance based on the classification accuracy. The results showed that the visual and visual-electrotactile stimulation feedback induced subject-specific changes in brain activation patterns and network reorganization in the α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} band. Thus, the visual-electrotactile stimulation feedback significantly improved the integration of information flow between brain regions associated with motor-related commands and higher-level cognitive functions, while reducing cognitive workload in the sensory areas of the brain and promoting positive emotions. Despite these promising results, neither neurofeedback modality resulted in a significant improvement in classification accuracy, compared with the absence of feedback. These findings indicate that multimodal neurofeedback can modulate imagery-mediated rehabilitation by enhancing motor-cognitive communication and reducing cognitive effort. In future interventions, incorporating this technique to ease cognitive demands for participants could be crucial for maintaining their motivation to engage in rehabilitation.
... Altered small-world properties of the surface-based brain network in patients with FCon Functional brain networks are characterized by specific topological features, with C P and L P being crucial components for assessing small-worldness network parameters (Mheich et al., 2020). Regular networks typically exhibit high C P and long L P , Frontiers in Neuroscience 07 frontiersin.org ...
Background
Functional constipation (FCon) is a common functional gastrointestinal disorder (FGID). Studies have indicated a higher likelihood of psychiatric disorders, such as anxiety, depression, sleep disturbances, and impaired concentration, among patients with FCon. However, the underlying pathophysiological mechanisms responsible for these symptoms in FCon patients remain to be fully elucidated. The human brain is a complex network architecture with several fundamental organizational properties. Neurological interactions between gut symptoms and psychiatric issues may be closely associated with these complex networks.
Methods
In the present study, a total of 35 patients with FCon and 40 healthy controls (HC) were recruited for a series of clinical examinations and resting-state functional magnetic imaging (RS-fMRI). We employed the surface-based analysis (SBA) approach, utilizing the Schaefer cortical parcellation template and Tikhonov regularization. Graph theoretical analysis (GTA) and functional connectivity (FC) analysis of RS-fMRI were conducted to investigate the aberrant network alterations between the two groups. Additionally, correlation analyses were performed between the network indices and clinical variables in patients with FCon.
Results
At the global level, we found altered topological properties and networks in patients with FCon, mainly including the significantly increased clustering coefficient (CP), local efficiency (Eloc), and shortest path length (LP), whereas the decreased global efficiency (Eglob) compared to HC. At the regional level, patients with FCon exhibited increased nodal efficiency in the frontoparietal network (FPN). Furthermore, FC analysis demonstrated several functional alterations within and between the Yeo 7 networks, particularly including visual network (VN), limbic network (LN), default mode network (DMN), and somatosensory-motor network (SMN) in sub-network and large-scale network analysis. Correlation analysis revealed that there were no significant associations between the network metrics and clinical variables in the present study.
Conclusion
These results highlight the altered topological architecture of functional brain networks associated with visual perception abilities, emotion regulation, sensorimotor processing, and attentional control, which may contribute to effectively targeted treatment modalities for patients with FCon.
... In order to further investigate the temporal sequence of snapshot functional brain networks, different approaches may be adopted. Estimating distance or (dis-)similarity between two networks might be one such approach, although finding suitable distance metrics still remains a challenge (Mheich et al., 2020). Another approach consists of the so-far insufficiently studied concept of multilayer networks (De Frontiers in Network Physiology frontiersin.org ...
Biological rhythms are natural, endogenous cycles with period lengths ranging from less than 24 h (ultradian rhythms) to more than 24 h (infradian rhythms). The impact of the circadian rhythm (approximately 24 h) and ultradian rhythms on spectral characteristics of electroencephalographic (EEG) signals has been investigated for more than half a century. Yet, only little is known on how biological rhythms influence the properties of EEG-derived evolving functional brain networks. Here, we derive such networks from multiday, multichannel EEG recordings and use different centrality concepts to assess the time-varying importance hierarchy of the networks' vertices and edges as well as the various aspects of their structural integration in the network. We observe strong circadian and ultradian influences that highlight distinct subnetworks in the evolving functional brain networks. Our findings indicate the existence of a vital and fundamental subnetwork that is rather generally involved in ongoing brain activities during wakefulness and sleep.
... However, it is reasonable to suggest that measures of proximity or (dis-)similarity may be used to index the signal-to-noise ratio yielded by different window size settings. These include the Pearson correlation [13], graph theoretic distance metrics such as geodesic [14] distance, and a recent algorithm that considers the physical location of the nodes not just their value, SimiNet [15], see [16] for a recent review. Here, we address the optimal window size problem for functional connectivity analysis of: (1) infant vs adult neural EEG data, with dyadic interaction as our particular interest case and (2) linear vs nonlinear connectivity metrics. ...
... Thus far, comparing networks is a notoriously difficult task, particularly for networks of different sizes (and changes in network sizes often go hand in hand with these perturbations), and there is no commonly accepted and sufficient way to do so. 47,48 Hence, we can only focus on network metrics 49 that, in total, describe the network somewhat comprehensively (cf. Sec. ...
Constructing networks from empirical time-series data is often faced with the as yet unsolved issue of how to avoid potentially superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system's dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from global to local scale. We derive a perturbation-based method to identify potentially superfluous network constituents that makes use of vertex and edge centrality concepts. We investigate the suitability of our approach through analyses of weighted small-world, scale-free, random, and complete networks. Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0152030 Understanding complex dynamical systems such as climate and brain profits from the network approach. Deriving networks from measurements of the systems' dynamics, however, can lead to spurious indications of network properties, depending on the employed sampling strategies and time-series analysis techniques to define network constituents. This, together with limitations in knowledge about the system's actual structural organization, calls for approaches to identify potentially superfluous network constituents. Here, we present such an approach. It is based on minuscule and elementary perturbations targeting single network constituents. Constituents are deemed potentially superfluous if the perturbations lead to no or only negligible changes of network characteristics, covering the local to global scale. We test our approach on various paradigmatic network models.
... However, it is reasonable to suggest that measures of proximity or (dis-)similarity may be used to index the signal-to-noise ratio yielded by different window size settings. These include the Pearson correlation [13], graph theoretic distance metrics such as geodesic [14] distance, and a recent algorithm that considers the physical location of the nodes not just their value, SimiNet [15], see [16] for a recent review. Here, we address the optimal window size problem for functional connectivity analysis of: (1) infant vs adult neural EEG data, with dyadic interaction as our particular interest case and (2) linear vs nonlinear connectivity metrics. ...
Neural connectivity analysis is often performed on continuous data that has been discretized into temporal windows of a fixed length. However, the selection of an optimal window length is non-trivial, and depends on the properties of the connectivity metric being used as well as the effects of interest within the data (e.g. developmental or inter-brain effects). A systematic investigation of these factors, and objective criteria for window size selection are currently missing in the literature, particularly in regard to pediatric datasets. Here, we provide a principled examination of the effect of window size on optimization of signal to noise ratio for linear and non-linear EEG connectivity, as applied to infant, adult and dyadic (infant-adult) datasets. We employed a linear weighted phase lag index (wPLI), and a nonlinear weighted symbolic mutual information (wSMI) metric to assess brain connectivity for each dataset. Our results showed a clear polar dissociation between linear and non-linear metrics, as well as between infant and adult datasets in optimal window size. Further, optimal dyadic (infant-adult) window size settings defaulted to one or the partner rather than reflecting an intermediate compromise. Given the specificity of these results (i.e. there was no single window size that was optimal for all contrasts), we conclude that a formal analysis of optimal window size may be useful prior to conducting any new connectivity analysis. Here, we recommend guiding principles, performance metrics and decision criteria for optimal and unbiased window
size selection.
... Here, we apply a continuous graph dissimilarity metric known as D-measure [36] which ranges from 0 to 1 (isomorphic). Dmeasure has been applied to analyze social networks [37,38], community structures [39], brain networks [40], and to characterize structural transition of zeolite nanoporous materials [41]. ...
... Nonetheless, and especially when it comes to the investigation of real-world systems, it remains unclear, how on a general basis minuscule perturbations targeting single constituents change the respective networks. Thus far, comparing networks is a notorious difficult task, particularly for networks of different sizes (and changes in network sizes often go hand in hand with these perturbations) and there is no commonly accepted and sufficient way to do so 47,48 . Hence, we can only focus on network metrics 49 that, in total, describe the network somewhat comprehensively (cf. ...
Constructing networks from empirical time series data is often faced with the as yet unsolved issue of how to avoid potentially superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system's dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from global to local scale. We derive a perturbation-based method to identify potentially superfluous network constituents that makes use of vertex and edge centrality concepts. We investigate the suitability of our approach through analyses of weighted small-world, scale-free, random, and complete networks.
... The number of connections between subjects from the same group (N = 72) in this graph is greater than the number of connections between subjects from different groups (N = 74) (Mheich et al. 2020). To filter the edges with the highest similarity, a threshold value is used. ...
Schizophrenia is a psychiatric disorder characterized by symptoms such as disorganized thinking, hallucinations, disintegration of reality perception, and delusions, among others. Resting-state functional magnetic resonance imaging is a promising method for studying changes in functional brain networks in schizophrenic patients. Graph theoretic representations can effectively distinguish between healthy and schizophrenic subjects. The process of grouping users with similar interests in social networks, which can also be used to group diseased subjects, is known as community detection. In this paper, we propose a method for classifying schizophrenia and normal subjects from fMRI images by employing graph similarity and community detection algorithms. The fMRI images are first preprocessed to remove noise, and then the automated anatomical labelling atlas is used to divide the human brain into 116 regions. Following that, a region connectivity matrix is constructed, and a weighted undirected graph is generated from the connectivity matrix. The graph similarity algorithm is then used to determine the similarity between each graph or subject. Then, a network of networks is built, which is a weighted network in which each graph is a node, and the top k (threshold) similarity scores between the graphs form the graph’s edges. On the newly constructed weighted graph, a community detection algorithm is used to detect communities that classify schizophrenia and normal subjects. We applied this proposed method to the COBRE dataset, which is publicly available and consists of 72 schizophrenic patients and 74 healthy subjects. We achieved an accuracy of 86.5% and compared it to other graph-based methods.
