Performance of modularity maximization in practical contexts

Consistency and differences between centrality measures across distinct classes of networks

The roles of different nodes within a network are often understood through centrality analysis, which aims to quantify the capacity of a node to influence, or be influenced by, other nodes via its connection topology. Many different centrality measures have been proposed, but the degree to which they offer unique information, and whether it is advantageous to use multiple centrality measures to define node roles, is unclear. Here we calculate correlations between 17 different centrality measures across 212 diverse real-world networks, examine how these correlations relate to variations in network density and global topology, and investigate whether nodes can be clustered into distinct classes according to their centrality profiles. We find that centrality measures are generally positively correlated to each other, the strength of these correlations varies across networks, and network modularity plays a key role in driving these cross-network variations. Data-driven clustering of nodes based on centrality profiles can distinguish different roles, including topological cores of highly central nodes and peripheries of less central nodes. Our findings illustrate how network topology shapes the pattern of correlations between centrality measures and demonstrate how a comparative approach to network centrality can inform the interpretation of nodal roles in complex networks.

Emergence of polarized opinions from free association networks

We developed a method that can identify polarized public opinions by finding modules in a network of statistically related free word associations. Associations to the cue “migrant” were collected from two independent and comprehensive samples in Hungary (N₁ = 505, N₂ = 505). The co-occurrence-based relations of the free word associations reflected emotional similarity, and the modules of the association network were validated with well-established measures. The positive pole of the associations was gathered around the concept of “Refugees” who need help, whereas the negative pole associated asylum seekers with “Violence.” The results were relatively consistent in the two independent samples. We demonstrated that analyzing the modular organization of association networks can be a tool for identifying the most important dimensions of public opinion about a relevant social issue without using predefined constructs.

Network-driven differences in mobility and optimal transitions among automatable jobs

The potential for widespread job automation has become an important topic of discussion in recent years, and it is thought that many American workers may need to learn new skills or transition to new jobs to maintain stable positions in the workforce. Because workers' existing skills may make such transitions more or less difficult, the likelihood of a given job being automated only tells part of the story. As such, this study uses network science and statistics to investigate the links between jobs that arise from their necessary skills, knowledge and abilities. The resulting network structure is found to enhance the burden of automation within some sectors while lessening the burden in others. Additionally, a model is proposed for quantifying the expected benefit of specific job transitions. Its optimization reveals that the consideration of shared skills yields better transition recommendations than automatability and job growth alone. Finally, the potential benefit of increasing individual skills is quantified, with respect to facilitating both job transitions and within-occupation skill redefinition. Broadly, this study presents a framework for measuring the links between jobs and demonstrates the importance of these links for understanding the complex effects of automation.

Reconfiguration of Cortical Networks in MDD Uncovered by Multiscale Community Detection with fMRI

Major depressive disorder (MDD) is known to be associated with altered interactions between distributed brain regions. How these regional changes relate to the reorganization of cortical functional systems, and their modulation by antidepressant medication, is relatively unexplored. To identify changes in the community structure of cortical functional networks in MDD, we performed a multiscale community detection algorithm on resting-state functional connectivity networks of unmedicated MDD (uMDD) patients (n = 46), medicated MDD (mMDD) patients (n = 38), and healthy controls (n = 50), which yielded a spectrum of multiscale community partitions. we selected an optimal resolution level by identifying the most stable community partition for each group. uMDD and mMDD groups exhibited a similar reconfiguration of the community structure of the visual association and the default mode systems but showed different reconfiguration profiles in the frontoparietal control (FPC) subsystems. Furthermore, the central system (somatomotor/salience) and 3 frontoparietal subsystems showed strengthened connectivity with other communities in uMDD but, with the exception of 1 frontoparietal subsystem, returned to control levels in mMDD. These findings provide evidence for reconfiguration of specific cortical functional systems associated with MDD, as well as potential effects of medication in restoring disease-related network alterations, especially those of the FPC system.

Multi-scale detection of hierarchical community architecture in structural and functional brain networks

Community detection algorithms have been widely used to study the organization of complex networks like the brain. These techniques provide a partition of brain regions (or nodes) into clusters (or communities), where nodes within a community are densely interconnected with one another. In their simplest application, community detection algorithms are agnostic to the presence of community hierarchies: clusters embedded within clusters of other clusters. To address this limitation, we exercise a multi-scale extension of a common community detection technique, and we apply the tool to synthetic graphs and to graphs derived from human neuroimaging data, including structural and functional imaging data. Our multi-scale community detection algorithm links a graph to copies of itself across neighboring topological scales, thereby becoming sensitive to conserved community organization across levels of the hierarchy. We demonstrate that this method is sensitive to topological inhomogeneities of the graph's hierarchy by providing a local measure of community stability and inter-scale reliability across topological scales. We compare the brain's structural and functional network architectures, and we demonstrate that structural graphs display a more prominent hierarchical community organization than functional graphs. Finally, we build an explicitly multimodal multiplex graph that combines both structural and functional connectivity in a single model, and we identify the topological scales where resting state functional connectivity and underlying structural connectivity show similar versus unique hierarchical community architecture. Together, our results demonstrate the advantages of the multi-scale community detection algorithm in studying hierarchical community structure in brain graphs, and they illustrate its utility in modeling multimodal neuroimaging data.

Decreased integration of EEG source-space networks in disorders of consciousness

Increasing evidence links disorders of consciousness (DOC) with disruptions in functional connectivity between distant brain areas. However, to which extent the balance of brain network segregation and integration is modified in DOC patients remains unclear. Using high-density electroencephalography (EEG), the objective of our study was to characterize the local and global topological changes of DOC patients' functional brain networks.

Resting state high-density-EEG data were collected and analyzed from 82 participants: 61 DOC patients recovering from coma with various levels of consciousness (EMCS (n = 6), MCS+ (n = 29), MCS- (n = 17) and UWS (n = 9)), and 21 healthy subjects (i.e., controls). Functional brain networks in five different EEG frequency bands and the broadband signal were estimated using an EEG connectivity approach at the source level. Graph theory-based analyses were used to evaluate their relationship with decreasing levels of consciousness as well as group differences between healthy volunteers and DOC patient groups.

Results showed that networks in DOC patients are characterized by impaired global information processing (network integration) and increased local information processing (network segregation) as compared to controls. The large-scale functional brain networks had integration decreasing with lower level of consciousness.

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Long-distance communication between brain regions is altered in patients suffering from disorders of consciousness.

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Impaired consciousness is associated with disruptions in brain network integration.

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The left orbitofrontal and left precuneus were identified in all patients groups.

Electroconvulsive therapy "corrects" the neural architecture of visuospatial memory: Implications for typical cognitive-affective functioning

Although electroconvulsive therapy (ECT) is a widely used and effective treatment for refractory depression, the neural underpinnings of its therapeutic effects remain poorly understood. To address this issue, here, we focused on a core cognitive deficit associated with depression, which tends to be reliably ameliorated through ECT, specifically, the ability to learn visuospatial information. Thus, we pursued three goals. First, we tested whether ECT can "normalize" the functional brain organization patterns associated with visuospatial memory and whether such corrections would predict post-ECT improvements in learning visuospatial information. Second, we investigated whether, among healthy individuals, stronger expression of the neural pattern, susceptible to adjustments through ECT, would predict reduced incidence of depression-relevant cognition and affect. Third, we sought to quantify the heritability of the ECT-correctable neural profile. Thus, in a task fMRI study with a clinical and a healthy comparison sample, we characterized two functional connectome patterns: one that typifies trait depression (i.e., differentiates patients from healthy individuals) and another that is susceptible to "normalization" through ECT. Both before and after ECT, greater expression of the trait depression neural profile was associated with more frequent repetitive thinking about past personal events (affective persistence), a hallmark of depressogenic cognition. Complementarily, post-treatment, stronger expression of the ECT-corrected neural profile was linked to improvements in visuospatial learning, a mental ability which is markedly impaired in depression. Subsequently, using data from the Human Connectome Project (HCP) (N = 333), we demonstrated that the functional brain organization of healthy participants with greater levels of subclinical depression and higher incidence of its associated cognitive deficits (affective persistence, impaired learning) shows greater similarity to the trait depression neural profile and reduced similarity to the ECT-correctable neural profile, as identified in the patient sample. These results tended to be specific to learning-relevant task contexts (working memory, perceptual relational processing). Genetic analyses based on HCP twin data (N = 128 pairs) suggested that, among healthy individuals, a functional brain organization similar to the one normalized by ECT in the patient sample is endogenous to cognitive contexts that require visuospatial processing that extends beyond the here-and-now. Broadly, the present findings supported our hypothesis that some of the therapeutic effects of ECT may be due to its correcting the expression of a naturally occurring pattern of functional brain organization that facilitates integration of internal and external cognition beyond the immediate present. Given their substantial susceptibility to both genetic and environmental effects, such mechanisms may be useful both for identifying at risk individuals and for monitoring progress of interventions targeting mood-related pathology.

From Louvain to Leiden: guaranteeing well-connected communities

Community detection is often used to understand the structure of large and complex networks. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. To address this problem, we introduce the Leiden algorithm. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. In addition, we prove that, when the Leiden algorithm is applied iteratively, it converges to a partition in which all subsets of all communities are locally optimally assigned. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees.

The impact of fasting on resting state brain networks in mice

Fasting is known to influence learning and memory in mice and alter the neural networks that subserve these cognitive functions. We used high-resolution functional MRI to study the impact of fasting on resting-state functional connectivity in mice following 12 h of fasting. The cortex and subcortex were parcellated into 52 subregions and functional connectivity was measured between each pair of subregions in groups of fasted and non-fasted mice. Functional connectivity was globally increased in the fasted group compared to the non-fasted group, with the most significant increases evident between the hippocampus (bilateral), retrosplenial cortex (left), visual cortex (left) and auditory cortex (left). Functional brain networks in the non-fasted group comprised five segregated modules of strongly interconnected subregions, whereas the fasted group comprised only three modules. The amplitude of low frequency fluctuations (ALFF) was decreased in the ventromedial hypothalamus in the fasted group. Correlation in gamma oscillations derived from local field potentials was increased between the left visual and retrosplenial cortices in the fasted group and the power of gamma oscillations was reduced in the ventromedial hypothalamus. These results indicate that fasting induces profound changes in functional connectivity, most likely resulting from altered coupling of neuronal gamma oscillations.

The intrinsic neural architecture of inhibitory control: The role of development and emotional experience

Inhibitory control is a key determinant of goal-directed behavior. Its susceptibility to reward implies that its variations may not only reflect cognitive ability, but also sensitivity to goal-relevant information. Since cognitive ability and motivational sensitivity vary as a function of age and mood, we hypothesized that their relevance for predicting individual differences in inhibition would similarly vary. Here, we tested this prediction with respect to the brain's intrinsic functional architecture. Specifically, we reasoned that age and affective functioning would both moderate the relationship between inhibition and resting state expression of the dynamic neural organization patterns linked to engaging in cognitive effort versus those involved in manipulating motivationally salient information. First, we used task fMRI data from the Human Connectome Project (N = 359 participants) to identify the brain organization patterns unique to effortful cognitive processing versus manipulation of motivationally relevant information. We then assessed the association between inhibitory control and relative expression of these two neural patterns in an independent resting state dataset from the Nathan Kline Institute-Rockland lifespan sample (N = 247). As hypothesized, the relation between inhibition and intrinsic functional brain architecture varied as a function of age and affective functioning. Among those with superior affective functioning, better inhibitory control in adolescence and early adulthood was associated with stronger resting state expression of the brain pattern that typified processing of motivationally salient information. The opposite effect emerged beyond the age of 49. Among individuals with poorer affective functioning, a significant link between inhibition and brain architecture emerged only before the age of 28. In this group, superior inhibition was associated with stronger resting state expression of the neural pattern that typified effortful cognitive processing. Our results thus imply that motivational relevance makes a unique contribution to superior cognitive functioning during earlier life stages. However, its relevance to higher-order mentation decreases with aging and increased prevalence of mood-related problems, which raises the possibility that patterns of neurobehavioral responsiveness to motivational salience may constitute sensitive markers of successful lifespan development.

Counting the number of metastable states in the modularity landscape: Algorithmic detectability limit of greedy algorithms in community detection

Modularity maximization using greedy algorithms continues to be a popular approach toward community detection in graphs, even after various better forming algorithms have been proposed. Apart from its clear mechanism and ease of implementation, this approach is persistently popular because, presumably, its risk of algorithmic failure is not well understood. This Rapid Communication provides insight into this issue by estimating the algorithmic performance limit of the stochastic block model inference using modularity maximization. This is achieved by counting the number of metastable states under a local update rule. Our results offer a quantitative insight into the level of sparsity at which a greedy algorithm typically fails.

A nature inspired modularity function for unsupervised learning involving spatially embedded networks

The quality of network clustering is often measured in terms of a commonly used metric known as "modularity". Modularity compares the clusters found in a network to those present in a random graph (a "null model"). Unfortunately, modularity is somewhat ill suited for studying spatially embedded networks, since a random graph contains no basic geometrical notions. Regardless of their distance, the null model assigns a nonzero probability for an edge to appear between any pair of nodes. Here, we propose a variant of modularity that does not rely on the use of a null model. To demonstrate the essentials of our method, we analyze networks generated from granular ensemble. We show that our method performs better than the most commonly used Newman-Girvan (NG) modularity in detecting the best (physically transparent) partitions in those systems. Our measure further properly detects hierarchical structures, whenever these are present.

Co-Association Matrix-Based Multi-Layer Fusion for Community Detection in Attributed Networks

Community detection is a challenging task in attributed networks, due to the data inconsistency between network topological structure and node attributes. The problem of how to effectively and robustly fuse multi-source heterogeneous data plays an important role in community detection algorithms. Although some algorithms taking both topological structure and node attributes into account have been proposed in recent years, the fusion strategy is simple and usually adopts the linear combination method. As a consequence of this, the detected community structure is vulnerable to small variations of the input data. In order to overcome this challenge, we develop a novel two-layer representation to capture the latent knowledge from both topological structure and node attributes in attributed networks. Then, we propose a weighted co-association matrix-based fusion algorithm (WCMFA) to detect the inherent community structure in attributed networks by using multi-layer fusion strategies. It extends the community detection method from a single-view to a multi-view style, which is consistent with the thinking model of human beings. Experiments show that our method is superior to the state-of-the-art community detection algorithms for attributed networks.

De novo clustering of long reads by gene from transcriptomics data

Long-read sequencing currently provides sequences of several thousand base pairs. It is therefore possible to obtain complete transcripts, offering an unprecedented vision of the cellular transcriptome. However the literature lacks tools for de novo clustering of such data, in particular for Oxford Nanopore Technologies reads, because of the inherent high error rate compared to short reads. Our goal is to process reads from whole transcriptome sequencing data accurately and without a reference genome in order to reliably group reads coming from the same gene. This de novo approach is therefore particularly suitable for non-model species, but can also serve as a useful pre-processing step to improve read mapping. Our contribution both proposes a new algorithm adapted to clustering of reads by gene and a practical and free access tool that allows to scale the complete processing of eukaryotic transcriptomes. We sequenced a mouse RNA sample using the MinION device. This dataset is used to compare our solution to other algorithms used in the context of biological clustering. We demonstrate that it is the best approach for transcriptomics long reads. When a reference is available to enable mapping, we show that it stands as an alternative method that predicts complementary clusters.

The landscape of NeuroImage-ing research

As the field of neuroimaging grows, it can be difficult for scientists within the field to gain and maintain a detailed understanding of its ever-changing landscape. While collaboration and citation networks highlight important contributions within the field, the roles of and relations among specific areas of study can remain quite opaque. Here, we apply techniques from network science to map the landscape of neuroimaging research documented in the journal NeuroImage over the past decade. We create a network in which nodes represent research topics, and edges give the degree to which these topics tend to be covered in tandem. The network displays small-world architecture, with communities characterized by common imaging modalities and medical applications, and with hubs that integrate these distinct subfields. Using node-level analysis, we quantify the structural roles of individual topics within the neuroimaging landscape, and find high levels of clustering within the structural MRI subfield as well as increasing participation among topics related to psychiatry. The overall prevalence of a topic is unrelated to the prevalence of its neighbors, but the degree to which a topic becomes more or less popular over time is strongly related to changes in the prevalence of its neighbors. Finally, we incorporate data from PNAS to investigate whether it serves as a trend-setter for topics' use within NeuroImage. We find that popularity trends are correlated across the two journals, and that changes in popularity tend to occur earlier within PNAS among growing topics. Broadly, this work presents a cohesive model for understanding the emergent relationships and dynamics of research topics within NeuroImage.

Time-evolving dynamics in brain networks forecast responses to health messaging

Neuroimaging measures have been used to forecast complex behaviors, including how individuals change decisions about their health in response to persuasive communications, but have rarely incorporated metrics of brain network dynamics. How do functional dynamics within and between brain networks relate to the processes of persuasion and behavior change? To address this question, we scanned 45 adult smokers by using functional magnetic resonance imaging while they viewed anti-smoking images. Participants reported their smoking behavior and intentions to quit smoking before the scan and 1 month later. We focused on regions within four atlas-defined networks and examined whether they formed consistent network communities during this task (measured as allegiance). Smokers who showed reduced allegiance among regions within the default mode and fronto-parietal networks also demonstrated larger increases in their intentions to quit smoking 1 month later. We further examined dynamics of the ventromedial prefrontal cortex (vmPFC), as activation in this region has been frequently related to behavior change. The degree to which vmPFC changed its community assignment over time (measured as flexibility) was positively associated with smoking reduction. These data highlight the value in considering brain network dynamics for understanding message effectiveness and social processes more broadly.

Global vs local modularity for network community detection

Community structures are ubiquitous in various complex networks, implying that the networks commonly be composed of groups of nodes with more internal links and less external links. As an important topic in network theory, community detection is of importance for understanding the structure and function of the networks. Optimizing statistical measures for community structures is one of most popular strategies for community detection in complex networks. In the paper, by using a type of self-loop rescaling strategy, we introduced a set of global modularity functions and a set of local modularity functions for community detection in networks, which are optimized by a kind of the self-consistent method. We carefully compared and analyzed the behaviors of the modularity-based methods in community detection, and confirmed the superiority of the local modularity for detecting community structures on large-size and heterogeneous networks. The local modularity can more quickly eliminate the first-type limit of modularity, and can eliminate or alleviate the second-type limit of modularity in networks, because of the use of the local information in networks. Moreover, we tested the methods in real networks. Finally, we expect the research can provide useful insight into the problem of community detection in complex networks.

Critical analysis of (Quasi-)Surprise for community detection in complex networks

Module or community structures widely exist in complex networks, and optimizing statistical measures is one of the most popular approaches for revealing and identifying such structures in real-world applications. In this paper, we focus on critical behaviors of (Quasi-)Surprise, a type of statistical measure of interest for community structure, accompanied by a series of comparisons with other measures. Specially, the effect of various network parameters on the measures is thoroughly investigated. The critical number of dense subgraphs in partition transition is derived, and a kind of phase diagrams is provided to display and compare the phase transitions of the measures. The effect of “potential well” for (Quasi-)Surprise is revealed, which may be difficult to get across by general greedy (agglomerative or divisive) algorithms. Finally, an extension of Quasi-Surprise is introduced for the study of multi-scale structures. Experimental results are of help for understanding the critical behaviors of (Quasi-)Surprise, and may provide useful insight for the design of effective tools for community detection.

Dynamic reshaping of functional brain networks during visual object recognition

OBJECTIVE

Emerging evidence shows that the modular organization of the human brain allows for better and efficient cognitive performance. Many of these cognitive functions are very fast and occur in a sub-second time scale such as the visual object recognition.

APPROACH

Here, we investigate brain network modularity while controlling stimuli meaningfulness and measuring a participant's reaction time. We particularly raised two questions: i) does the dynamic brain network modularity change during the recognition of meaningful and meaningless visual images? And (ii) is there a correlation between network modularity and the reaction time of the participants? To tackle these issues, we collected dense-electroencephalography (EEG, 256 channels) data from 20 healthy human subjects performing a cognitive task consisting of naming meaningful (tools, animals…) and meaningless (scrambled) images. Functional brain networks in both categories were estimated at the sub-second time scale using the EEG source connectivity method. By using multislice modularity algorithms, we tracked the reconfiguration of functional networks during the recognition of both meaningful and meaningless images.

MAIN RESULTS

Results showed a difference in the module's characteristics of both conditions in term of integration (interactions between modules) and occurrence (probability on average of any two brain regions to fall in the same module during the task). Integration and occurrence were greater for meaningless than for meaningful images. Our findings revealed also that the occurrence within the right frontal regions and the left occipito-temporal can help to predict the ability of the brain to rapidly recognize and name visual stimuli.

SIGNIFICANCE

We speculate that these observations are applicable not only to other fast cognitive functions but also to detect fast disconnections that can occur in some brain disorders.

Comparative analysis on the selection of number of clusters in community detection

We conduct a comparative analysis on various estimates of the number of clusters in community detection. An exhaustive comparison requires testing of all possible combinations of frameworks, algorithms, and assessment criteria. In this paper we focus on the framework based on a stochastic block model, and investigate the performance of greedy algorithms, statistical inference, and spectral methods. For the assessment criteria, we consider modularity, map equation, Bethe free energy, prediction errors, and isolated eigenvalues. From the analysis, the tendency of overfit and underfit that the assessment criteria and algorithms have becomes apparent. In addition, we propose that the alluvial diagram is a suitable tool to visualize statistical inference results and can be useful to determine the number of clusters.

Network Controllability in the Inferior Frontal Gyrus Relates to Controlled Language Variability and Susceptibility to TMS

In language production, humans are confronted with considerable word selection demands. Often, we must select a word from among similar, acceptable, and competing alternative words to construct a sentence that conveys an intended meaning. In recent years, the left inferior frontal gyrus (LIFG) has been identified as being critical to this ability. Despite a recent emphasis on network approaches to understanding language, how the LIFG interacts with the brain's complex networks to facilitate controlled language performance remains unknown. Here, we take a novel approach to understanding word selection as a network control process in the brain. Using an anatomical brain network derived from high-resolution diffusion spectrum imaging, we computed network controllability underlying the site of transcranial magnetic stimulation (TMS) in the LIFG between administrations of language tasks that vary in response (cognitive control) demands: open-response tasks (word generation) versus closed response tasks (number naming). We found that a statistic that quantifies the LIFG's theoretically predicted control of communication across modules in the human connectome explains TMS-induced changes in open-response language task performance only. Moreover, we found that a statistic that quantifies the LIFG's theoretically predicted control of difficult-to-reach states explains vulnerability to TMS in the closed-ended (but not open-ended) response task. These findings establish a link among network controllability, cognitive function, and TMS effects.SIGNIFICANCE STATEMENT This work illustrates that network control statistics applied to anatomical connectivity data demonstrate relationships with cognitive variability during controlled language tasks and TMS effects.

Default mode network abnormalities in posttraumatic stress disorder: A novel network-restricted topology approach

Disruption in the default mode network (DMN) has been implicated in numerous neuropsychiatric disorders, including posttraumatic stress disorder (PTSD). However, studies have largely been limited to seed-based methods and involved inconsistent definitions of the DMN. Recent advances in neuroimaging and graph theory now permit the systematic exploration of intrinsic brain networks. In this study, we used resting-state functional magnetic resonance imaging (fMRI), diffusion MRI, and graph theoretical analyses to systematically examine the DMN connectivity and its relationship with PTSD symptom severity in a cohort of 65 combat-exposed US Veterans. We employed metrics that index overall connectivity strength, network integration (global efficiency), and network segregation (clustering coefficient). Then, we conducted a modularity and network-based statistical analysis to identify DMN regions of particular importance in PTSD. Finally, structural connectivity analyses were used to probe whether white matter abnormalities are associated with the identified functional DMN changes. We found decreased DMN functional connectivity strength to be associated with increased PTSD symptom severity. Further topological characterization suggests decreased functional integration and increased segregation in subjects with severe PTSD. Modularity analyses suggest a spared connectivity in the posterior DMN community (posterior cingulate, precuneus, angular gyrus) despite overall DMN weakened connections with increasing PTSD severity. Edge-wise network-based statistical analyses revealed a prefrontal dysconnectivity. Analysis of the diffusion networks revealed no alterations in overall strength or prefrontal structural connectivity. DMN abnormalities in patients with severe PTSD symptoms are characterized by decreased overall interconnections. On a finer scale, we found a pattern of prefrontal dysconnectivity, but increased cohesiveness in the posterior DMN community and relative sparing of connectivity in this region. The DMN measures established in this study may serve as a biomarker of disease severity and could have potential utility in developing circuit-based therapeutics.

Applications of community detection techniques to brain graphs: Algorithmic considerations and implications for neural function

The human brain can be represented as a graph in which neural units such as cells or small volumes of tissue are heterogeneously connected to one another through structural or functional links. Brain graphs are parsimonious representations of neural systems that have begun to offer fundamental insights into healthy human cognition, as well as its alteration in disease. A critical open question in network neuroscience lies in how neural units cluster into densely interconnected groups that can provide the coordinated activity that is characteristic of perception, action, and adaptive behaviors. Tools that have proven particularly useful for addressing this question are community detection approaches, which can identify communities or modules: groups of neural units that are densely interconnected with other units in their own group but sparsely interconnected with units in other groups. In this paper, we describe a common community detection algorithm known as modularity maximization, and we detail its applications to brain graphs constructed from neuroimaging data. We pay particular attention to important algorithmic considerations, especially in recent extensions of these techniques to graphs that evolve in time. After recounting a few fundamental insights that these techniques have provided into brain function, we highlight potential avenues of methodological advancements for future studies seeking to better characterize the patterns of coordinated activity in the brain that accompany human behavior. This tutorial provides a naive reader with an introduction to theoretical considerations pertinent to the generation of brain graphs, an understanding of modularity maximization for community detection, a resource of statistical measures that can be used to characterize community structure, and an appreciation of the usefulness of these approaches in uncovering behaviorally-relevant network dynamics in neuroimaging data.

Detecting phenotype-driven transitions in regulatory network structure

Complex traits and diseases like human height or cancer are often not caused by a single mutation or genetic variant, but instead arise from functional changes in the underlying molecular network. Biological networks are known to be highly modular and contain dense “communities” of genes that carry out cellular processes, but these structures change between tissues, during development, and in disease. While many methods exist for inferring networks and analyzing their topologies separately, there is a lack of robust methods for quantifying differences in network structure. Here, we describe ALPACA (ALtered Partitions Across Community Architectures), a method for comparing two genome-scale networks derived from different phenotypic states to identify condition-specific modules. In simulations, ALPACA leads to more nuanced, sensitive, and robust module discovery than currently available network comparison methods. As an application, we use ALPACA to compare transcriptional networks in three contexts: angiogenic and non-angiogenic subtypes of ovarian cancer, human fibroblasts expressing transforming viral oncogenes, and sexual dimorphism in human breast tissue. In each case, ALPACA identifies modules enriched for processes relevant to the phenotype. For example, modules specific to angiogenic ovarian tumors are enriched for genes associated with blood vessel development, and modules found in female breast tissue are enriched for genes involved in estrogen receptor and ERK signaling. The functional relevance of these new modules suggests that not only can ALPACA identify structural changes in complex networks, but also that these changes may be relevant for characterizing biological phenotypes.

Cells are controlled by complex regulatory networks, and disruptions in the structure of these networks can lead to disease. Understanding disease requires that we accurately identify changes in gene regulatory network structure. However, cellular networks have tens of thousands of components with complex connections between them. Megha Padi from the University of Arizona and John Quackenbush from Dana-Farber Cancer Institute developed a new algorithm that is far more effective than previous methods at finding disease-associated modules in regulatory networks. Applying this to ovarian cancer, they found new regulatory processes that may lead to more targeted treatments. In human breast tissue, they found that sex-specific differences were driven by hormone signaling and differentiation pathways. Decoding how network modules promote new functions may help to better model the relationship between genotype and phenotype.

Community Detection in Complex Networks via Clique Conductance

Network science plays a central role in understanding and modeling complex systems in many areas including physics, sociology, biology, computer science, economics, politics, and neuroscience. One of the most important features of networks is community structure, i.e., clustering of nodes that are locally densely interconnected. Communities reveal the hierarchical organization of nodes, and detecting communities is of great importance in the study of complex systems. Most existing community-detection methods consider low-order connection patterns at the level of individual links. But high-order connection patterns, at the level of small subnetworks, are generally not considered. In this paper, we develop a novel community-detection method based on cliques, i.e., local complete subnetworks. The proposed method overcomes the deficiencies of previous similar community-detection methods by considering the mathematical properties of cliques. We apply the proposed method to computer-generated graphs and real-world network datasets. When applied to networks with known community structure, the proposed method detects the structure with high fidelity and sensitivity. When applied to networks with no a priori information regarding community structure, the proposed method yields insightful results revealing the organization of these complex networks. We also show that the proposed method is guaranteed to detect near-optimal clusters in the bipartition case.

Accurate detection of hierarchical communities in complex networks based on nonlinear dynamical evolution

One of the most challenging problems in network science is to accurately detect communities at distinct hierarchical scales. Most existing methods are based on structural analysis and manipulation, which are NP-hard. We articulate an alternative, dynamical evolution-based approach to the problem. The basic principle is to computationally implement a nonlinear dynamical process on all nodes in the network with a general coupling scheme, creating a networked dynamical system. Under a proper system setting and with an adjustable control parameter, the community structure of the network would "come out" or emerge naturally from the dynamical evolution of the system. As the control parameter is systematically varied, the community hierarchies at different scales can be revealed. As a concrete example of this general principle, we exploit clustered synchronization as a dynamical mechanism through which the hierarchical community structure can be uncovered. In particular, for quite arbitrary choices of the nonlinear nodal dynamics and coupling scheme, decreasing the coupling parameter from the global synchronization regime, in which the dynamical states of all nodes are perfectly synchronized, can lead to a weaker type of synchronization organized as clusters. We demonstrate the existence of optimal choices of the coupling parameter for which the synchronization clusters encode accurate information about the hierarchical community structure of the network. We test and validate our method using a standard class of benchmark modular networks with two distinct hierarchies of communities and a number of empirical networks arising from the real world. Our method is computationally extremely efficient, eliminating completely the NP-hard difficulty associated with previous methods. The basic principle of exploiting dynamical evolution to uncover hidden community organizations at different scales represents a "game-change" type of approach to addressing the problem of community detection in complex networks.

The timing and causes of a unique chimpanzee community fission preceding Gombe's "Four-Year War"

OBJECTIVES

While permanent group fissions are documented in humans and other primate species, they are relatively rare in male philopatric primates. One of the few apparent cases occurred in 1973 in Gombe National Park, Tanzania, when a community of chimpanzees split into two separate groups, preceding the famous "Four-Year War." We tested the hypothesis that the original group was a single cohesive community that experienced permanent fission, and investigated several potential catalysts.

MATERIALS AND METHODS

We calculated association, grooming, and ranging metrics from historical data and used community detection algorithms and matrix permutation tests to determine the timing, dynamics, and causes of changes in social network subgrouping structure.

RESULTS

We found that the two communities indeed split from one cohesive community, albeit one with incipient subgrouping. The degree of subgrouping in grooming and association networks increased sharply in 1971 and 1972, a period characterized by a dominance struggle between three high-ranking males and unusually high male:female sex ratios. Finally, we found a relationship between post-split community membership and previous association, grooming and ranging patterns in most periods of analysis, one that became more pronounced as the fission approached.

DISCUSSION

Our analysis suggests that the community began to split during a time of an unusually male-biased sex ratio and a protracted dominance struggle, and that adult males remained with those with whom they had preferentially associated prior to the split. We discuss the costs and benefits of group membership in chimpanzees and contrast these results with group fissions in humans and other taxa.

Tracking the Reorganization of Module Structure in Time-Varying Weighted Brain Functional Connectivity Networks

Identification of module structure in brain functional networks is a promising way to obtain novel insights into neural information processing, as modules correspond to delineated brain regions in which interactions are strongly increased. Tracking of network modules in time-varying brain functional networks is not yet commonly considered in neuroscience despite its potential for gaining an understanding of the time evolution of functional interaction patterns and associated changing degrees of functional segregation and integration. We introduce a general computational framework for extracting consensus partitions from defined time windows in sequences of weighted directed edge-complete networks and show how the temporal reorganization of the module structure can be tracked and visualized. Part of the framework is a new approach for computing edge weight thresholds for individual networks based on multiobjective optimization of module structure quality criteria as well as an approach for matching modules across time steps. By testing our framework using synthetic network sequences and applying it to brain functional networks computed from electroencephalographic recordings of healthy subjects that were exposed to a major balance perturbation, we demonstrate the framework’s potential for gaining meaningful insights into dynamic brain function in the form of evolving network modules. The precise chronology of the neural processing inferred with our framework and its interpretation helps to improve the currently incomplete understanding of the cortical contribution for the compensation of such balance perturbations.

Dynamic Flexibility in Striatal-Cortical Circuits Supports Reinforcement Learning

Complex learned behaviors must involve the integrated action of distributed brain circuits. Although the contributions of individual regions to learning have been extensively investigated, much less is known about how distributed brain networks orchestrate their activity over the course of learning. To address this gap, we used fMRI combined with tools from dynamic network neuroscience to obtain time-resolved descriptions of network coordination during reinforcement learning in humans. We found that learning to associate visual cues with reward involves dynamic changes in network coupling between the striatum and distributed brain regions, including visual, orbitofrontal, and ventromedial prefrontal cortex (n = 22; 13 females). Moreover, we found that this flexibility in striatal network coupling correlates with participants' learning rate and inverse temperature, two parameters derived from reinforcement learning models. Finally, we found that episodic learning, measured separately in the same participants at the same time, was related to dynamic connectivity in distinct brain networks. These results suggest that dynamic changes in striatal-centered networks provide a mechanism for information integration during reinforcement learning.SIGNIFICANCE STATEMENT Learning from the outcomes of actions, referred to as reinforcement learning, is an essential part of life. The roles of individual brain regions in reinforcement learning have been well characterized in terms of updating values for actions or cues. Missing from this account, however, is an understanding of how different brain areas interact during learning to integrate sensory and value information. Here we characterize flexible striatal-cortical network dynamics that relate to reinforcement learning behavior.

Revisiting the Functional and Structural Connectivity of Large-Scale Cortical Networks

Multimodal neuroimaging research has become increasingly popular, and structure-function correspondence is tacitly assumed. Researchers have not yet adequately assessed whether the functional connectivity (FC) and structural connectivity (SC) of large-scale cortical networks are in agreement. Structural magnetic resonance imaging (sMRI), resting-state functional MRI (rfMRI), and diffusion-weighted imaging (DWI) data sets from 36 healthy subjects (age 27.4) were selected from a Rockland sample (Enhanced Nathan Kline Institute). The cerebral cortex was parcellated into 62 regions according to the Desikan-Killiany atlas for FC and SC analyses. Thresholded correlations in rfMRI and tractography derived from DWI were used to construct FC and SC maps, respectively. A community detection algorithm was applied to reveal the underlying organization, and modular consistency was quantified to bridge cross-modal comparisons. The distributions of correlation coefficients in FC and SC maps were significantly different. Approximately one-fourth of the connections in the SC map were located at a correlation level below 0.2 (df 253). The index of modular consistency in the within-modality interindividual condition (either FC or SC) was considerably greater than that in the between-modality intraindividual analog. In addition, the SC-FC differential map (SC connections with lower correlations) revealed reliable modular structures. Based on these results, the hypothesized FC-SC agreement is partially valid. Contingent on extant neuroimaging tools and analytical conventions, the neural informatics of FC and SC should be regarded as complementary rather than concordant. Furthermore, the results verify the physiological significance of moderately (or mildly) correlated brain signals in rfMRI, which are often discarded by stringent thresholding.

Locally stable brain states predict suppression of epileptic activity by enhanced cognitive effort

Cognitive effort is known to play a role in healthy brain state organization, but little is known about its effects on pathological brain dynamics. When cortical stimulation is used to map functional brain areas prior to surgery, a common unwanted side effect is the appearance of afterdischarges (ADs), epileptiform and potentially epileptogenic discharges that can progress to a clinical seizure. It is therefore desirable to suppress this activity. Here, we analyze electrocorticography recordings from 15 patients with epilepsy. We show that a cognitive intervention in the form of asking an arithmetic question can be effective in suppressing ADs, but that its effectiveness is dependent upon the brain state at the time of intervention. By applying novel techniques from network analysis to quantify brain states, we find that the spatial organization of ADs with respect to coherent brain regions relates to the success of the cognitive intervention: if ADs are mainly localized within a single stable brain region, a cognitive intervention is likely to suppress the ADs. These findings show that cognitive effort is a useful tactic to modify unstable pathological activity associated with epilepsy, and suggest that the success of therapeutic interventions to alter activity may depend on an individual's brain state at the time of intervention.

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Cognitive intervention in the form of an arithmetic question can sometimes stop epileptic afterdischarges

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Brain states are measured through community structure of functional brain networks

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Success of intervention depends on spatial relationship between afterdischarge network and brain state

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Dynamic community detection is used to assess community stability

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If the afterdischarge network is in a strong, stable community, the cognitive intervention likely stops the afterdischarges

Multiresolution Consensus Clustering in Networks

Networks often exhibit structure at disparate scales. We propose a method for identifying community structure at different scales based on multiresolution modularity and consensus clustering. Our contribution consists of two parts. First, we propose a strategy for sampling the entire range of possible resolutions for the multiresolution modularity quality function. Our approach is directly based on the properties of modularity and, in particular, provides a natural way of avoiding the need to increase the resolution parameter by several orders of magnitude to break a few remaining small communities, necessitating the introduction of ad-hoc limits to the resolution range with standard sampling approaches. Second, we propose a hierarchical consensus clustering procedure, based on a modified modularity, that allows one to construct a hierarchical consensus structure given a set of input partitions. While here we are interested in its application to partitions sampled using multiresolution modularity, this consensus clustering procedure can be applied to the output of any clustering algorithm. As such, we see many potential applications of the individual parts of our multiresolution consensus clustering procedure in addition to using the procedure itself to identify hierarchical structure in networks.

Detecting hierarchical genome folding with network modularity

Mammalian genomes are folded in a hierarchy of compartments, topologically associating domains (TADs), subTADs and looping interactions. Here, we describe 3DNetMod, a graph theory-based method for sensitive and accurate detection of chromatin domains across length scales in Hi-C data. We identify nested, partially overlapping TADs and subTADs genome wide by optimizing network modularity and varying a single resolution parameter. 3DNetMod can be applied broadly to understand genome reconfiguration in development and disease.

Structure, function, and control of the human musculoskeletal network

The human body is a complex organism, the gross mechanical properties of which are enabled by an interconnected musculoskeletal network controlled by the nervous system. The nature of musculoskeletal interconnection facilitates stability, voluntary movement, and robustness to injury. However, a fundamental understanding of this network and its control by neural systems has remained elusive. Here we address this gap in knowledge by utilizing medical databases and mathematical modeling to reveal the organizational structure, predicted function, and neural control of the musculoskeletal system. We constructed a highly simplified whole-body musculoskeletal network in which single muscles connect to multiple bones via both origin and insertion points. We demonstrated that, using this simplified model, a muscle's role in this network could offer a theoretical prediction of the susceptibility of surrounding components to secondary injury. Finally, we illustrated that sets of muscles cluster into network communities that mimic the organization of control modules in primary motor cortex. This novel formalism for describing interactions between the muscular and skeletal systems serves as a foundation to develop and test therapeutic responses to injury, inspiring future advances in clinical treatments.

Brain state flexibility accompanies motor-skill acquisition

Learning requires the traversal of inherently distinct cognitive states to produce behavioral adaptation. Yet, tools to explicitly measure these states with non-invasive imaging – and to assess their dynamics during learning – remain limited. Here, we describe an approach based on a distinct application of graph theory in which points in time are represented by network nodes, and similarities in brain states between two different time points are represented as network edges. We use a graph-based clustering technique to identify clusters of time points representing canonical brain states, and to assess the manner in which the brain moves from one state to another as learning progresses. We observe the presence of two primary states characterized by either high activation in sensorimotor cortex or high activation in a frontal-subcortical system. Flexible switching among these primary states and other less common states becomes more frequent as learning progresses, and is inversely correlated with individual differences in learning rate. These results are consistent with the notion that the development of automaticity is associated with a greater freedom to use cognitive resources for other processes. Taken together, our work offers new insights into the constrained, low dimensional nature of brain dynamics characteristic of early learning, which give way to less constrained, high-dimensional dynamics in later learning.

Aging and Network Properties: Stability Over Time and Links with Learning during Working Memory Training

Growing evidence suggests that healthy aging affects the configuration of large-scale functional brain networks. This includes reducing network modularity and local efficiency. However, the stability of these effects over time and their potential role in learning remain poorly understood. The goal of the present study was to further clarify previously reported age effects on "resting-state" networks, to test their reliability over time, and to assess their relation to subsequent learning during training. Resting-state fMRI data from 23 young (YA) and 20 older adults (OA) were acquired in 2 sessions 2 weeks apart. Graph-theoretic analyses identified both consistencies in network structure and differences in module composition between YA and OA, suggesting topological changes and less stability of functional network configuration with aging. Brain-wide, OA showed lower modularity and local efficiency compared to YA, consistent with the idea of age-related functional dedifferentiation, and these effects were replicable over time. At the level of individual networks, OA consistently showed greater participation and lower local efficiency and within-network connectivity in the cingulo-opercular network, as well as lower intra-network connectivity in the default-mode network and greater participation of the somato-sensorimotor network, suggesting age-related differential effects at the level of specialized brain modules. Finally, brain-wide network properties showed associations, albeit limited, with learning rates, as assessed with 10 days of computerized working memory training administered after the resting-state sessions, suggesting that baseline network configuration may influence subsequent learning outcomes. Identification of neural mechanisms associated with learning-induced plasticity is important for further clarifying whether and how such changes predict the magnitude and maintenance of training gains, as well as the extent and limits of cognitive transfer in both younger and older adults.

Network size, structure, and pathogen transmission: a simulation study comparing different community detection algorithms

Social substructure can influence pathogen transmission. Modularity measures the degree of social contact within versus between “communities” in a network, with increasing modularity expected to reduce transmission opportunities. We investigated how social substructure scales with network size and disease transmission. Using small-scale primate social networks, we applied seven community detection algorithms to calculate modularity and subgroup cohesion, defined as individuals’ interactions within subgroups proportional to the network. We found larger networks were more modular with higher subgroup cohesion, but the association’s strength varied by community detection algorithm and substructure measure. These findings highlight the importance of choosing an appropriate community detection algorithm for the question of interest, and if not possible, using multiple algorithms. Disease transmission simulations revealed higher modularity and subgroup cohesion resulted in fewer infections, confirming that social substructure has epidemiological consequences. Increased subdivision in larger networks could reflect constrained time budgets or evolved defences against disease risk.

Dynamical networks: Finding, measuring, and tracking neural population activity using network science

Systems neuroscience is in a headlong rush to record from as many neurons at the same time as possible. As the brain computes and codes using neuron populations, it is hoped these data will uncover the fundamentals of neural computation. But with hundreds, thousands, or more simultaneously recorded neurons come the inescapable problems of visualizing, describing, and quantifying their interactions. Here I argue that network science provides a set of scalable, analytical tools that already solve these problems. By treating neurons as nodes and their interactions as links, a single network can visualize and describe an arbitrarily large recording. I show that with this description we can quantify the effects of manipulating a neural circuit, track changes in population dynamics over time, and quantitatively define theoretical concepts of neural populations such as cell assemblies. Using network science as a core part of analyzing population recordings will thus provide both qualitative and quantitative advances to our understanding of neural computation.

Beyond modularity: Fine-scale mechanisms and rules for brain network reconfiguration

The human brain is in constant flux, as distinct areas engage in transient communication to support basic behaviors as well as complex cognition. The collection of interactions between cortical and subcortical areas forms a functional brain network whose topology evolves with time. Despite the nontrivial dynamics that are germane to this networked system, experimental evidence demonstrates that functional interactions organize into putative brain systems that facilitate different facets of cognitive computation. We hypothesize that such dynamic functional networks are organized around a set of rules that constrain their spatial architecture - which brain regions may functionally interact - and their temporal architecture - how these interactions fluctuate over time. To objectively uncover these organizing principles, we apply an unsupervised machine learning approach called non-negative matrix factorization to time-evolving, resting state functional networks in 20 healthy subjects. This machine learning approach automatically groups temporally co-varying functional interactions into subgraphs that represent putative topological modes of dynamic functional architecture. We find that subgraphs are stratified based on both the underlying modular organization and the topographical distance of their strongest interactions: while many subgraphs are largely contained within modules, others span between modules and are expressed differently over time. The relationship between dynamic subgraphs and modular architecture is further highlighted by the ability of time-varying subgraph expression to explain inter-individual differences in module reorganization. Collectively, these results point to the critical role that subgraphs play in constraining the topography and topology of functional brain networks. More broadly, this machine learning approach opens a new door for understanding the architecture of dynamic functional networks during both task and rest states, and for probing alterations of that architecture in disease.

Brain state expression and transitions are related to complex executive cognition in normative neurodevelopment

Adolescence is marked by rapid development of executive function. Mounting evidence suggests that executive function in adults may be driven by dynamic control of neurophysiological processes. Yet, how these dynamics evolve over adolescence and contribute to cognitive development is unknown. In a sample of 780 youth aged 8-22 yr (42.7% male) from the Philadelphia Neurodevelopment Cohort, we use a dynamic graph approach to extract activation states in BOLD fMRI data from 264 brain regions. We construct a graph in which each observation in time is a node and the similarity in brain states at two different times is an edge. Using this graphical approach, we identify two primary brain states reminiscent of intrinsic and task-evoked systems. We show that time spent in these two states is higher in older adolescents, as is the flexibility with which the brain switches between them. Increasing time spent in primary states and flexibility among states relates to increases in a complex executive accuracy factor score over adolescence. Flexibility is more positively associated with accuracy toward early adulthood. These findings suggest that brain state dynamics are associated with complex executive function across a critical period of adolescence.