Network Neuroscience

Brain network formation unfolds on a non-uniform developmental timetable, with different cortical regions generating connections at different developmental phases. Generative network models (GNMs) aim to uncover the principles underpinning the organisation of connectomes by creating synthetic networks according to simple computational rules. These models capture the connectomes topology, operationalised here as the overall distributions of network metrics (e.g., modularity, small-worldness, rich-club structure). However, they typically ignore the differential timing of connectivity formation. By omitting this temporal programme, GNMs often misplace topological features in physical space. Here, we add a heterochronous growth term to GNMs and use a new model fitness function that weighs topology and topography equally. Topography refers to the spatial embedding of the network, the actual anatomical positions of tracts. With these advances, we can generate synthetic networks that more faithfully reproduce the spatial layout of diffusion-MRI connectomes from two independent adult cohorts. Compared with classical, temporally agnostic models, heterochronous simulations improve model fit, accurately locate cortical hubs and modules, and converge on a single caudal-to-rostral gradient of brain maturation. Integrating heterochronicity makes GNMs more faithful to brain development, setting the stage for using them to explain and ultimately predict individual differences in network formation.

Connectomes are the structural scaffold for signalling within nervous systems. While many network models have been proposed to describe connectome communication, current approaches assume that every pair of neural elements communicates according to the same principle. Connectomes, however, are heterogeneous networks, comprising elements with varied topological and neurobiological makeups. In this paper, we investigate how connectome architecture may facilitate different signalling regimes depending on the topological embedding of communicating neural elements. Specifically, we test the hypothesis that the modular structure of brain networks fosters a dual mode of communication balancing diffusion--passive signal broadcasting--and routing--selective transmission via efficient paths. To this end, we introduce the relative diffusion score (RDS), a measure to quantify the proportional capacity for network communication via diffusion versus routing. We examined the interplay between RDS and connectome architecture in 6 organisms spanning a wide range of spatial resolutions and connectivity mapping techniques--from the complete nervous system of the larval fly to the inter-areal human connectome. Our analyses establish multiple lines of evidence suggesting that connectomes may be universally organised to support within-module diffusion and between-module routing. Using a series of rewiring null models, we untangle the contributions of connectome topology and geometry to the relationship between routing, diffusion and modular architecture. In conclusion, our work puts forth a hybrid conceptualisation of neural communication, in which diffusion contributes to functional segregation by concentrating information within localised clusters, while specialised signal routes enable fast, long-range and cross-system functional integration.

The white matter is made of anatomical fibres that constitute the highway of long-range connections between different parts of the brain. This network is referred to as the brains structural connectivity and lays the foundation of network interaction between brain areas. When analysing the architectural principles of this global network most studies have mainly focused on cortico-cortical and partly on cortico-subcortical connections. Here we show, for the first time, how the integrated cortical, subcortical, and cerebellar brain areas shape the structural architecture of the whole brain. We find that dense clusters vertically transverse cortical, subcortical, and cerebellar brain areas, which are themselves centralised by a global rich-club consisting similarly of cortical and subcortical brain areas. Notably, the most prominent hubs can be found in subcortical brain regions, and their targeted in-silico lesions proved to be most harmful for global signal propagation. Individually, the cortical, subcortical, and cerebellar sub-networks manifest distinct network features despite some similarities, which underline their unique structural fingerprints. Our results, exposing the heterogeneity of internal organisation across cortex, subcortex, and cerebellum, and the crucial role of the subcortex for the integration of the global anatomical pathways, highlight the need to overcome the prevalent cortex-centric focus towards a global consideration of the structural connectivity.

We present MesoSCOUT (Mesoscale Structural Connectome Order-complex Unveiling Topology), a framework for characterizing white matter connectivity using a method developed from computational algebraic topology: persistent homology (PH) via clique topology. Applying this method to schizophrenia, we uncover a novel, mesoscale perspective of the differences in the white-matter connectome between healthy controls (HC) and subjects with schizophrenia (SCH). We extract and compare topological motifs found in the structural connectomes of the subjects in the two groups and find significant differences. We explore the overlap of mesoscale structures found in two different datasets, COBRE (Center of Biomedical Research Excellence) and HCP (Human Connectome Project). Differences in acquisition usually render experiments recorded on different scanners incomparable, but MesoSCOUT enables cross-dataset comparisons. Our method offers a way to establish connectomic fingerprinting that could lead to a neuroimaging-based diagnosis of schizophrenia and other psychiatric and neurological conditions as well as the development of new treatments.

General intelligence, referred to as g, is hypothesized to emerge from the capacity to dynamically and adaptively reorganize macroscale brain connectivity. Temporal reconfiguration can be assessed using dynamic functional connectivity (dFC), which captures the propensity of brain connectivity to transition between a recurring repertoire of distinct states. Conventional dFC metrics commonly focus on categorical state switching frequencies which do not fully assess individual variation in continuous connectivity reconfiguration. Here, we supplement frequency measures by quantifying within-state connectivity consistency, dissimilarity between connectivity across states, and conformity of individual connectivity to group-average state connectivity. We utilized resting-state fMRI data from the large-scale Human Connectome Project and applied data-driven multivariate Partial Least Squares Correlation to explore emergent associations between dynamic network properties and cognitive ability. Our findings reveal a positive association between g and the stable maintenance of states characterized by distinct connectivity between higher-order networks, efficient reconfiguration (i.e., minimal connectivity changes during transitions between similar states, large connectivity changes between dissimilar states), and ability to sustain connectivity close to group-average state connectivity. This hints at fundamental properties of brain-behavior organization, suggesting that general cognitive processing capacity is supported by the ability to efficiently reconfigure between stable and population-typical connectivity patterns. Impact StatementNovel evidence for an association between the stability, efficiency, and typicality of macro-scale dynamic functional connectivity patterns of the brain and higher general intelligence.

Structural connectivity between cortical areas, as revealed by tract-tracing is in the form of highly dense, weighted, directed, and spatially embedded complex networks. Extracting the community structure of these networks and aligning them with brain function is challenging, as most methods use local density measures, best suited for sparse graphs. Here we introduce a principled approach, based on distinguishability of connectivity profiles using the Hellinger distance, which is relatable to function. Applying it to tract-tracing data in the macaque, we show that the cortex at the interareal level is organized into a nested hierarchy of link-communities alongside with a node-community hierarchy. We find that the [1/2]-Renyi divergence of connection profiles, a non-linear transform of the Hellinger metric, follows a Weibull-like distribution and scales linearly with the interareal distances, a quantitative expression between functional organization and cortical geometry. We discuss the relationship with the extensively studied SLN-based hierarchy.

How communication among neuronal ensembles shapes functional brain dynamics at the large scale is a question of fundamental importance to Neuroscience. To date, researchers have primarily relied on two alternative ways to address this issue 1) in-silico neurodynamical modelling of functional brain dynamics by choosing biophysically inspired non-linear systems, interacting via a connection topology driven by empirical data; and 2) identifying topological measures to quantify network structure and studying them in tandem with functional metrics of interest, e.g. co-variation of time series in brain regions from fast (EEG/ MEG) and slow (fMRI) timescales. While the modelling approaches are limited in scope to only scales of the nervous system for which dynamical models are well defined, the latter approach does not take into account how the network architecture and intrinsic regional node dynamics contribute together to inter-regional communication in the brain. Thus, developing a generalized scale-invariant measure of interaction between network topology and constituent regional dynamics can potentially resolve how transmission of perturbations in brain networks alter function e.g. by neuropathologies, or the intervention strategies designed to mitigate them. In this work, we introduce a recently developed theoretical perturbative framework in network science into a neuroscientific framework, to conceptualize the interaction of regional dynamics and network architecture in a quantifiable manner. This framework further provides insights into the information communication contributions of putative regions and sub-networks in the brain, irrespective of the observational scale of the phenomenon (firing rates to BOLD fMRI time series). The proposed approach can directly quantify network-dynamical interactions without reliance on a specific class of models or response characteristics: linear/nonlinear. By simply gauging the asymmetries in responses to perturbations, we obtain insights into the significance of regions in communication and their influence over the rest of the network. Moreover, coupling perturbations with functional lesions can also answer which regions contribute the most to information spread: a quantity termed Flow. The simplicity of the proposed technique allows translation to an experimental setting where the response asymmetries and flow can inversely act as a window into the dynamics of regions. For proof-of-concept, we apply the perturbative approach on in-silico data generated for human resting state network dynamics, using different established dynamical models that mimic empirical observations. We also apply the perturbation approach at the level of large scale Resting State Networks (RSNs) to gauge the range of network-dynamical interactions in mediating information flow across brain regions.

In this work, we propose a new class of graph measures for weighted connectivity information in the human brain based on node relative strengths: relative strength variability (RSV), measuring susceptibility to targeted attacks, and hierarchical RSV (hRSV), a first weighted statistical complexity measure for networks. Using six different network weights for structural connectomes from the UK Biobank, we conduct comprehensive analyses to explore relationships between the RSV and hRSV, and (i) other known network measures, (ii) general cognitive function ( g). Both measures exhibit low correlations with other graph measures across all connectivity weightings indicating that they capture new information of the brain connectome. We found higher g was associated with lower RSV and lower hRSV. That is, higher g was associated with higher resistance to targeted attack and lower statistical complexity. Moreover, the proposed measures had consistently stronger associations with g than other widely used graph measures including clustering coefficient and global efficiency and were incrementally significant for predicting g above other measures for five of the six network weights. Overall, we present a new class of weighted network measures based on variations of relative node strengths which significantly improved prediction of general cognition from traditional weighted structural connectomes.

Cerebral cortical networks in the mammalian brain exhibit a non-random organization in which reciprocal projections, although widespread, are systematically asymmetric in strength: feedforward connections are consistently stronger than their feedback counterparts, particularly in sensory cortices. This "no-strong-loops" principle is thought to prevent runaway excitation and maintain stability, yet its actual computational impact remains unclear. Here, we use computational analysis and modeling to show that connectivity asymmetry supports high working-memory capacity, whereas increasing reciprocity reduces memory capacity and representational diversity in reservoir-computing models of recurrent neural networks. We systematically examine synthetic architectures inspired by mammalian cortical connectivity and find that sparse, modular, and hierarchical networks achieve superior performance, relative to random, small-world, or core-periphery graphs, but only when reciprocity is constrained. Validated on directed mammalian (macaque, marmoset, rat, and mouse) connectomes, these results indicate that restricting reciprocal motifs yields functional benefits in sparse networks, consistent with an evolutionary strategy for stable, efficient information processing in the brain. These findings suggest a biologically-inspired design principle for artificial neural systems.

The Allen mesoscale mouse brain structural connectome is analysed using standard network methods combined with 3D visualizations. The full region-to-region connectivity data is used, with a focus on the strongest structural links. The spatial embedding of links and time evolution of signalling is incorporated, with two-step links included. Modular decomposition using the Infomap method produces 8 network modules that correspond approximately to major brain anatomical regions and system functions. These modules align with the anterior and posterior primary sensory systems and association areas. 3D visualization of network links is facilitated by using a set of simplified schematic coordinates that reduces visual complexity. Selection of key nodes and links, such as sensory pathways and cortical association areas together reveal structural features of the mouse structural connectome consistent with biological functions in the sensory-motor systems, and selective roles of the anterior and posterior cortical association areas of the mouse brain. Time progression of signals along sensory pathways reveals that close links are to local cortical association areas and cross modal, while longer links provide anterior-posterior coordination and inputs to non cortical regions. The fabric of weaker links generally are longer range with some having brain-wide reach. Cortical gradients are evident along sensory pathways within the structural network.\n\nAuthors SummaryNetwork models incorporating spatial embedding and signalling delays are used to investigate the mouse structural connectome. Network models that include time respecting paths are used to trace signaling pathways and reveal separate roles of shorter vs. longer links. Here computational methods work like experimental probes to uncover biologically relevant features. I use the Infomap method, which follows random walks on the network, to decompose the directed, weighted network into 8 modules that align with classical brain anatomical regions and system functions. Primary sensory pathways and cortical association areas are separated into individual modules. Strong, short range links form the sensory-motor paths while weaker links spread brain-wide, possibly coordinating many regions.

Interacting sets of nodes and fluctuations in their interaction are important properties of a dynamic network system. In some cases the edges reflecting these interactions are directly quantifiable from the data collected. However, in many cases (such as functional magnetic resonance imaging (fMRI) data), the edges must be inferred from statistical relations between the nodes. Here we present a new method, Temporal Communities through Trajectory Clustering (TCTC), that derives time-varying communities directly from time-series data collected from the nodes in a network. First, we verify TCTC on resting and task fMRI data by showing that time-averaged results correspond with expected static connectivity results. We then show that the time-varying communities correlate and predict single-trial behaviour. This new perspective on temporal community detection of node-collected data identifies robust communities revealing ongoing spatiotemporal community configurations during task performance.

The brains ability to transition between functional states while maintaining both flexibility and stability is shaped by its structural connectivity. Understanding the relationship between brain structure and neural dynamics is a central challenge in neuroscience. Prior studies link neural dynamics to local noisy activity and mesoscale coupling mechanisms, but causal links at the whole-brain scale remain elusive. This study investigates how the balance between integration and segregation in brain networks influences their dynamical properties, focusing on multistability (switching between stable states) and metastability (transient stability over time). We analyzed a spectrum of network models, from highly segregated to highly integrated, using structural metrics like modularity, efficiency, and small-worldness. Simulating neural activity with a neural mass model and analyzing Functional Connectivity Dynamics (FCD), we found that segregated networks sustain dynamic synchronization patterns, while small-world networks, which balance local clustering and global efficiency, exhibit the richest dynamical behavior. Networks with intermediate small-worldness ({omega}) values showed peak dynamical richness, measured by variance in FCD and metastability. Using Mutual Information (MI), we quantified the structure-dynamics relationship, revealing that modularity is the strongest predictor of network dynamics, as modular architectures support transitions between dynamical states. These findings underscore the importance of the small-world architecture in brain networks, where the balance between local specialization and global integration fosters the dynamic complexity necessary for cognitive functions. By emphasizing the role of modularity, this study enhances understanding of how structural features shape neural dynamics and offers insights into disruptions linked to neurological disorders.

It has been proposed that the estimation of the normalized graph Laplacian over a brain networks spectral decomposition can reveal the connectome harmonics (eigenvectors) corresponding to certain frequencies (eigenvalues). Here, I used test-retest dMRI data from the Human Connectome Project to explore the repeatability, and the influence of graph construction schemes on a) graph Laplacian spectrum, b) topological properties, c) high-order interactions (3,4-motifs,odd-cycles), and d) their associations on structural brain networks (SBN). Additionally, I investigated the performance of subjects identification accuracy (brain fingerprinting) of the graph Laplacian spectrum, the topological properties, and the high-order interactions. Normalized Laplacian eigenvalues were found to be subject-specific and repeatable across the five graph construction schemes. The repeatability of connectome harmonics is lower than that of the Laplacian eigenvalues and shows a heavy dependency on the graph construction scheme. A repeatable relationship between specific topological properties of the SBN with the Laplacian spectrum was also revealed. The identification accuracy of normalized Laplacian eigenvalues was absolute (100%) across the graph construction schemes, while a similar performance was observed for a combination of topological properties of SBN (communities,3,4-motifs, odd-cycles) only for the 9m-OMST. Collectively, Laplacian spectrum, topological properties, and high-order interactions characterized uniquely SBN.

Understanding whether the canonical topologies of macroscale connectomes, such as small-world architecture, hub dominance, rich-club cores, and modularity, extend to local cortical microcircuitry has remained challenging due to limitations in simultaneously recording large neuronal populations in vivo. Here, using ultra-large-scale, high-resolution calcium imaging, we tracked spontaneous activity from approximately 2,000 neurons across the mouse primary visual cortex (V1). Across multiple mice and correlation thresholds, V1 neuronal networks exhibited hallmark characteristics of efficient brain organization, but in a markedly intensified form compared to macroscopic brain networks. Local clustering coefficients remained an order of magnitude above random levels, while characteristic path lengths approached those observed in random networks, yielding an exceptionally high small-world index that substantially exceeded typical values previously reported at macroscopic scales. Degree distributions followed a power-law, identifying highly connected hub neurons whose interconnections formed a robust rich-club integrative core. Community detection analyses showed robust modularity upon pruning weak connections, indicating functionally specialized neuronal clusters interconnected predominantly through hubs. These findings provide one of the first direct in vivo evidence that single cortical microcircuits not only recapitulate but intensify network topologies observed at macroscopic scale, implying evolutionarily conserved design principles underlying brain organization from neurons to systems.

The hierarchical organization of the brains distributed network has received growing interest from the neuroscientific community, largely because of its potential to enhance our understanding of human cognition and behavior, in health and disease. This interest is motivated by the hypothesis that near-critical brain dynamics enable multiscale integration and segregation of neural dynamics. While most multiscale connectivity analyses focus on structural and functional networks, characterizing the effective connectome across multiple scales has been somewhat overlooked--primarily for computational reasons. The difficulty of estimating large cyclic causal models, together with the scarcity of theoretical frameworks for systematically moving between scales, has hindered progress in this direction. This technical note introduces a top-down multiscale parcellation scheme for dynamic causal models, with application to neuroimaging data. The method is based on Bayesian model comparison, as a generalization of the well-known {Delta}BIC method. To facilitate computation, recent developments in linear dynamic causal modeling (DCM) and Bayesian model reduction (BMR) are deployed. Specifically, a naive version of BMR is introduced, enabling the parcellation scheme to scale to hundreds or thousands of regions. Notably, the derivations reveal an analytical relationship between reduced model evidence and minimum cut problem in graph theory. This duality puts the tools of graph theory at the service of model evidence optimization and significance testing. The proposed method was applied to simulated and empirical causal models to establish face and construct validity. Consequently, the large empirical causal network, inferred from a neuroimaging dataset, exhibited log-log scaling trends, suggestive of scale invariance in multiple dynamical measures. Future generalizations of this technique and its potential applications in systems and clinical neuroscience are discussed.

Network neuroscience models the brain as interacting elements. However, a large number of elements imply a vast number of interactions, making it difficult to assess which connections are relevant and which are spurious. Zalesky et al. (2010) proposed the Network-Based Statistics (NBS), which identifies clusters of connections and tests their likelihood via permutation tests. This framework shows a better trade-off of Type I and II errors compared to conventional multiple comparison corrections. NBS uses General Linear Hypothesis Testing (GLHT), which may underestimate the within-subject variance structure when dealing with longitudinal samples with a varying number of observations (unbalanced samples). We implemented NBR, an R-package that extends the NBS framework adding (non)linear mixed-effects (LME) models. LME models the within-subject variance in more detail, and deals with missing values more flexibly. To illustrate its advantages, we used a public dataset of 333 human participants (188/145 females/males; age range: 17.0-28.4 y.o.) with two (n=212) or three (n=121) sessions each. Sessions include a resting-state fMRI scan and psychometric data. State anxiety scores and connectivity matrices between brain lobes were extracted. We tested their relationship using GLHT and LME models for balanced and unbalanced datasets, respectively. Only the LME approach found a significant association between state anxiety and a subnetwork that includes the cingulum, frontal, parietal, occipital, and cerebellum. Given that missing data is very common in longitudinal studies, we expect that NBR will be very useful to explore unbalanced samples. Significant StatementLongitudinal studies are increasing in neuroscience, providing new insights into the brain under treatment, development, or aging. Nevertheless, missing data is highly frequent in those studies, and conventional designs may discard incomplete observations or underestimate the within-subject variance. We developed a publicly available software (R package: NBR) that implements mixed-effect models into every possible connection in a sample of networks, and it can find significant subsets of connections using non-parametric permutation tests. We demonstrate that using NBR on larger unbalanced samples has higher statistical power than when exploring the balanced subsamples. Although this method is applicable in general network analysis, we anticipate this method being potentially useful in systems neuroscience considering the increase of longitudinal samples in the field.

Popular methods for analyzing the brains functional connectome examine statistical associations between pairs of atlas-defined brain regions, viewing the strength of these links as independent values. However, edges within a standard connectivity matrix, i.e., correlations between individual regions or nodes, are not independent. They are part of an interconnected system. Here, we propose that consideration of both independent, linear relationships (as in standard approaches such as linear kernel ridge regression and connectome-based predictive modeling) as well as higher order statistical associations - such as tertiary interactions between matrix components and global features of the matrix space - will enhance identification of meaningful individual differences. To test this, we adopt a geometrically grounded measure of similarity that accounts for higher-order local statistical relationships and global interactions, the Wasserstein metric. Results indicate that considering connectivity matrices as representations of their associated Gaussian distributions significantly improves both identification of individuals based on their connectivity matrices (aka, fingerprinting) and prediction of individual differences in phenotypes such as fluid intelligence and openness to experience. Thus, both pairwise local and global brain connectivity properties encode for meaningful individual differences that relate to phenotypic expressions and should be considered in brain-behavior predictive models.

Community detection provides a principled lens on mesoscale organization in functional brain networks, yet many widely used methods presume assortative structure and depend on arbitrary thresholding, which complicates the selection of the community count K. We conducted a systematic benchmark of three assumption lean approaches that operate directly on weighted functional connectivity matrices: the Weighted Stochastic Block Model, Spectral Clustering, and K-means. Performance was assessed on synthetic networks with known ground truth and on three neuroimaging cohorts spanning development, namely the Human Connectome Project, Washington University 120, and the Baby Connectome Project. We compared strategies for choosing K, including post hoc indices such as silhouette, Calinski-Harabasz, C index, modularity, variation of information, Normalized Mutual Information, and zRand, together with a likelihood-based criterion for the Weighted Stochastic Block Model that uses bootstrap confidence intervals for differences in log likelihood between successive values of K. In simulations all methods recovered stable partitions, but the post hoc indices favored incorrect values of K under weak signal and nonassortative mixing. In adult datasets the indices do not yield a unique optimum, whereas the likelihood-based criterion selects a parsimonious range centered near K = 11, which is consistent with established sensory and association systems. In infants and toddlers, the same procedure supports a larger K around 15 and reveals developmentally distinct mesoscale architecture, including anterior and posterior subdivisions within default mode and fronto parietal systems. A consensus relabeling scheme based on Hungarian matching with Hamming distance further stabilizes solutions across runs and across values of K. Overall, threshold free weighted methods mitigate assortative bias and the likelihood-based comparison provides a reproducible path to selecting K.

One of the fundamental challenges in modern neuroscience is understanding the interplay between the brains functional activity and its underlying structural pathways. To address this question, we propose a novel communication pattern called subnet communicability, which models diffusive communication between pairs of regions through a small, intermediary subnetwork of brain regions as opposed to spreading messages through the entire network. We demonstrate that subnet communicability strengthens coupling between the structural and functional connectomes better than previous models, including communicability. Over two large datasets, we show that the optimal subnetwork is consistent across the population. Subnet communicability provides new insights into structure-function coupling in the brain and offers a balance between redundancy in message passing and economy of brain wiring.

The quality of a childs social and physical environment is a key influence on brain development, educational attainment and mental wellbeing. However, there still remains a mechanistic gap in our understanding of how environmental influences converge on changes in the brains developmental trajectory. In a sample of 145 children with structural diffusion tensor imaging data, we used generative network modelling to simulate the emergence of whole brain network organisation. We then applied data-driven clustering to stratify the sample according to socio-economic disadvantage, with one of the resulting clusters containing mostly children living below the poverty line. A formal comparison of the simulated networks from the generative model revealed that the computational principles governing network formation were subtly different for children experiencing socio-economic disadvantage, and that this resulted in significantly altered developmental timing of network modularity emergence. Children in the low socio-economic status (SES) group had a significantly slower time to peak modularity, relative to the higher SES group (t(69) = 3.02, P = 3.50 x 10-4, d = 0.491). In a subsequent simulation we showed that the alteration in generative properties increases the variability in wiring probabilities during network formation (KS test: D = 0.012, P < 0.001). One possibility is that multiple environmental influences such as stress, diet and environmental stimulation impact both the systematic coordination of neuronal activity and biological resource constraints, converging on a shift in the economic conditions under which networks form. Alternatively, it is possible that this stochasticity reflects an adaptive mechanism that creates "resilient" networks better suited to unpredictable environments. Author SummaryWe used generative network models to simulate macroscopic brain network development in a sample of 145 children. Within these models, network connections form probabilistically depending on the estimated "cost" of forming a connection, versus topological "value" that the connection would confer. Tracking the formation of the network across the simulation, we could establish the changes in global brain organisation measures such as integration and segregation. Simulations for children experiencing socio-economic disadvantage were associated with a shift in emergence of a topologically valuable network property, namely modularity.