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One of the longstanding aims of network neuroscience is to link a connectome's topological properties-i.e., features defined from connectivity alone-with an organism's neurobiology. One approach for doing so is to compare connectome properties with annotational maps. This type of analysis is popular at the meso-/macroscale, but is less common at the nano-scale, owing to a paucity of neuron-level connectome data. However, recent methodological advances have made possible the reconstruction of whole-brain connectomes at single-neuron resolution for a select set of organisms. These include the fruit fly, Drosophila melanogaster , and its developing larvae. In addition to fine-scale descriptions of connectivity, these datasets are accompanied by rich annotations. Here, we use a variant of the stochastic blockmodel to detect multilevel communities in the larval Drosophila connectome. We find that communities partition neurons based on function and cell type and that most interact assortatively, reflecting the principle of functional segregation. However, a small number of communities interact nonassortatively, forming form a "rich-club" of interneurons that receive sensory/ascending inputs and deliver outputs along descending pathways. Next, we investigate the role of community structure in shaping communication patterns. We find that polysynaptic signaling follows specific trajectories across modular hierarchies, with interneurons playing a key role in mediating communication routes between modules and hierarchical scales. Our work suggests a relationship between system-level architecture and the biological function and classification of individual neurons. We envision our study as an important step toward bridging the gap between complex systems and neurobiological lines of investigation in brain sciences., Competing Interests: Competing interests statement:The authors declare no competing interest.

The brain connectome is an embedded network of anatomically interconnected brain regions, and the study of its topological organization in mammals has become of paramount importance due to its role in scaffolding brain function and behavior. Unlike many other observable networks, brain connections incur material and energetic cost, and their length and density are volumetrically constrained by the skull. Thus, an open question is how differences in brain volume impact connectome topology. We address this issue using the MaMI database, a diverse set of mammalian connectomes reconstructed from 201 animals, covering 103 species and 12 taxonomy orders, whose brain size varies over more than 4 orders of magnitude. Our analyses focus on relationships between volume and modular organization. After having identified modules through a multiresolution approach, we observed how connectivity features relate to the modular structure and how these relations vary across brain volume. We found that as the brain volume increases, modules become more spatially compact and dense, comprising more costly connections. Furthermore, we investigated how spatial embedding shapes network communication, finding that as brain volume increases, nodes' distance progressively impacts communication efficiency. We identified modes of variation in network communication policies, as smaller and bigger brains show higher efficiency in routing- and diffusion-based signaling, respectively. Finally, bridging network modularity and communication, we found that in larger brains, modular structure imposes stronger constraints on network signaling. Altogether, our results show that brain volume is systematically related to mammalian connectome topology and that spatial embedding imposes tighter restrictions on larger brains., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Puxeddu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

The standard approach to modeling the human brain as a complex system is with a network, where the basic unit of interaction is a pairwise link between two brain regions. While powerful, this approach is limited by the inability to assess higher-order interactions involving three or more elements directly. In this work, we explore a method for capturing higher-order dependencies in multivariate data: the partial entropy decomposition (PED). Our approach decomposes the joint entropy of the whole system into a set of nonnegative atoms that describe the redundant, unique, and synergistic interactions that compose the system's structure. PED gives insight into the mathematics of functional connectivity and its limitation. When applied to resting-state fMRI data, we find robust evidence of higher-order synergies that are largely invisible to standard functional connectivity analyses. Our approach can also be localized in time, allowing a frame-by-frame analysis of how the distributions of redundancies and synergies change over the course of a recording. We find that different ensembles of regions can transiently change from being redundancy-dominated to synergy-dominated and that the temporal pattern is structured in time. These results provide strong evidence that there exists a large space of unexplored structures in human brain data that have been largely missed by a focus on bivariate network connectivity models. This synergistic structure is dynamic in time and likely will illuminate interesting links between brain and behavior. Beyond brain-specific application, the PED provides a very general approach for understanding higher-order structures in a variety of complex systems.

Network models of anatomical connections allow for the extraction of quantitative features describing brain organization, and their comparison across brains from different species. Such comparisons can inform our understanding of between-species differences in brain architecture and can be compared to existing taxonomies and phylogenies. Here we performed a quantitative comparative analysis using the MaMI database (Tel Aviv University), a collection of brain networks reconstructed from ex vivo diffusion MRI spanning 125 species and 12 taxonomic orders or superorders. We used a broad range of metrics to measure between-mammal distances and compare these estimates to the separation of species as derived from taxonomy and phylogeny. We found that within-taxonomy order network distances are significantly closer than between-taxonomy network distances, and this relation holds for several measures of network distance. Furthermore, to estimate the evolutionary divergence between species, we obtained phylogenetic distances across 10,000 plausible phylogenetic trees. The anatomical network distances were rank-correlated with phylogenetic distances 10,000 times, creating a distribution of coefficients that demonstrate significantly positive correlations between network and phylogenetic distances. Collectively, these analyses demonstrate species-level organization across scales and informational sources: we relate brain networks distances, derived from MRI, with evolutionary distances, derived from genotyping data., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Faskowitz, Puxeddu, van den Heuvel, Mišić, Yovel, Assaf, Betzel and Sporns.)

The human brain is a complex network of anatomically interconnected brain areas. Spontaneous neural activity is constrained by this architecture, giving rise to patterns of statistical dependencies between the activity of remote neural elements. The non-trivial relationship between structural and functional connectivity poses many unsolved challenges about cognition, disease, development, learning and aging. While numerous studies have focused on statistical relationships between edge weights in anatomical and functional networks, less is known about dependencies between their modules and communities. In this work, we investigate and characterize the relationship between anatomical and functional modular organization of the human brain, developing a novel multi-layer framework that expands the classical concept of multi-layer modularity. By simultaneously mapping anatomical and functional networks estimated from different subjects into communities, this approach allows us to carry out a multi-subject and multi-modal analysis of the brain's modular organization. Here, we investigate the relationship between anatomical and functional modules during resting state, finding unique and shared structures. The proposed framework constitutes a methodological advance in the context of multi-layer network analysis and paves the way to further investigate the relationship between structural and functional network organization in clinical cohorts, during cognitively demanding tasks, and in developmental or lifespan studies., (Copyright © 2022 The Author(s). Published by Elsevier Inc. All rights reserved.)

The modular structure of brain networks supports specialized information processing, complex dynamics, and cost-efficient spatial embedding. Inter-individual variation in modular structure has been linked to differences in performance, disease, and development. There exist many data-driven methods for detecting and comparing modular structure, the most popular of which is modularity maximization. Although modularity maximization is a general framework that can be modified and reparamaterized to address domain-specific research questions, its application to neuroscientific datasets has, thus far, been narrow. Here, we highlight several strategies in which the "out-of-the-box" version of modularity maximization can be extended to address questions specific to neuroscience. First, we present approaches for detecting "space-independent" modules and for applying modularity maximization to signed matrices. Next, we show that the modularity maximization frame is well-suited for detecting task- and condition-specific modules. Finally, we highlight the role of multi-layer models in detecting and tracking modules across time, tasks, subjects, and modalities. In summary, modularity maximization is a flexible and general framework that can be adapted to detect modular structure resulting from a wide range of hypotheses. This article highlights multiple frontiers for future research and applications., (Copyright © 2021 The Authors. Published by Elsevier Inc. All rights reserved.)

Oscillatory activity rising from the interaction among neurons is widely observed in the brain at different scales and is thought to encode distinctive properties of the neural processing. Classical investigations of neuroelectrical activity and connectivity usually focus on specific frequency bands, considered as separate aspects of brain functioning. However, this might not paint the whole picture, preventing to see the brain activity as a whole, as the result of an integrated process. This study aims to provide a new framework for the analysis of the functional interaction between brain regions across frequencies and different subjects. We ground our work on the latest advances in graph theory, exploiting multi-layer community detection. In our multi-layer network model, layers keep track of single frequencies, including all the information in a unique graph. Community detection is then applied by means of a multilayer formulation of modularity. As a proof-of-concept of our approach, we provide here an application to multi-frequency functional brain networks derived from resting state EEG collected in a group of healthy subjects. Our results indicate that α-band selectively characterizes an inter-individual common organization of EEG brain networks during open eyes resting state. Future applications of this new approach may include the extraction of subject-specific features able to capture selected properties of the brain processes, related to physiological or pathological conditions.

Modular organization is an emergent property of brain networks, responsible for shaping communication processes and underpinning brain functioning. Moreover, brain networks are intrinsically multilayer since their attributes can vary across time, subjects, frequency, or other domains. Identifying the modular structure in multilayer brain networks represents a gateway toward a deeper understanding of neural processes underlying cognition. Electroencephalographic (EEG) signals, thanks to their high temporal resolution, can give rise to multilayer networks able to follow the dynamics of brain activity. Despite this potential, the community organization has not yet been thoroughly investigated in brain networks estimated from EEG. Furthermore, at the state of the art, there is still no agreement about which algorithm is the most suitable to detect communities in multilayer brain networks, and a way to test and compare them all under a variety of conditions is lacking. In this work, we perform a comprehensive analysis of three algorithms at the state of the art for multilayer community detection (namely, genLouvain, DynMoga, and FacetNet) as compared with an approach based on the application of a single-layer clustering algorithm to each slice of the multilayer network. We test their ability to identify both steady and dynamic modular structures. We statistically evaluate their performances by means of ad hoc benchmark graphs characterized by properties covering a broad range of conditions in terms of graph density, number of clusters, noise level, and number of layers. The results of this simulation study aim to provide guidelines about the choice of the more appropriate algorithm according to the different properties of the brain network under examination. Finally, as a proof of concept, we show an application of the algorithms to real functional brain networks derived from EEG signals collected at rest with closed and open eyes. The test on real data provided results in agreement with the conclusions of the simulation study and confirmed the feasibility of multilayer analysis of EEG-based brain networks in both steady and dynamic conditions., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Puxeddu, Petti and Astolfi.)

The network architecture of the human brain contributes in shaping neural activity, influencing cognitive and behavioral processes. The availability of neuroimaging data across the lifespan allows us to monitor how this architecture reorganizes, influenced by processes like learning, adaptation, maturation, and senescence. Changing patterns in brain connectivity can be analyzed with the tools of network science, which can be used to reveal organizational principles such as modular network topology. The identification of network modules is fundamental, as they parse the brain into coherent sub-systems and allow for both functional integration and segregation among different brain areas. In this work we examined the brain's modular organization by developing an ensemble-based multilayer network approach, allowing us to link changes of structural connectivity patterns to development and aging. We show that modular structure exhibits both linear and nonlinear age-related trends. In the early and late lifespan, communities are more modular, and we track the origins of this high modularity to two different substrates in brain connectivity, linked to the number and the weights of the intra-clusters edges. We also demonstrate that aging leads to a progressive and increasing reconfiguration of modules and a redistribution across hemispheres. Finally, we identify those brain regions that most contribute to network reconfiguration and those that remain more stable across the lifespan., Competing Interests: Declaration of competing interest The authors declare no conflicting interests., (Copyright © 2020 The Authors. Published by Elsevier Inc. All rights reserved.)

Community detection plays a key role in the study of brain networks, as mechanisms of modular integration and segregation are known to characterize the brain functioning. Moreover, brain networks are intrinsically multilayer: they can vary across time, frequency, subjects, conditions, and meaning, according to different definitions of connectivity. Several algorithms for the multilayer community detection were defined to identify communities in time-varying networks. The most used one is based on the optimization of a multilayer formulation of the modularity, in which two parameters linked to the spatial (γ) and temporal (ω) resolution of the uncovered communities can be set. While the effect of different γ-values has been largely explored, which ω-values are most suitable to different purposes and conditions is still an open issue. In this work, we test the algorithm performances under different values of ω by means of ad hoc implemented benchmark graphs that cover a wide range of conditions. Results provide a guide to the choice of the ω-values according to the network features. Finally, we show an application of the algorithm to real functional brain networks estimated from electro-encephalographic (EEG) signals collected at rest with closed and open eyes. The application to real data agrees with the results of the simulation study and confirms the conclusion drawn from it.

Community structure is a feature of complex networks that can be crucial for the understanding of their internal organization. This is particularly true for brain networks, as the brain functioning is thought to be based on a modular organization. In the last decades, many clustering algorithms were developed with the aim to identify communities in networks of different nature. However, there is still no agreement about which one is the most reliable, and to test and compare these algorithms under a variety of conditions would be beneficial to potential users. In this study, we performed a comparative analysis between six different clustering algorithms, analyzing their performances on a ground-truth consisting of simulated networks with properties spanning a wide range of conditions. Results show the effect of factors like the noise level, the number of clusters, the network dimension and density on the performances of the algorithms and provide some guidelines about the use of the more appropriate algorithm according to the different conditions. The best performances under a wide range of conditions were obtained by Louvain and Leicht & Newman algorithms, while Ronhovde and Infomap proved to be more appropriate in very noisy conditions. Finally, as a proof of concept, we applied the algorithms under exam to brain functional connectivity networks obtained from EEG signals recorded during a sustained movement of the right hand, obtaining a clustering of scalp electrodes which agrees with the results of the simulation study conducted.

Deep brain stimulation is a clinical technique for the treatment of parkinson's disease based on the electric stimulation, through an implanted electrode, of specific basal ganglia in the brain. To identify the correct target of stimulation and to choose the optimal parameters for the stimulating signal, intraoperative microelectrodes are generally used. However, when they are replaced with the chronic macroelectrode, the effect of the stimulation is often very different. Here, we used numerical simulations to predict the stimulation of neuronal fibers induced by microelectrodes and macroelectrodes placed in different positions with respect to each other. Results indicate that comparable stimulations can be obtained if the chronic macroelectrode is correctly positioned with the same electric center of the intraoperative microelectrode. Otherwise, some groups of fibers may experience a completely different electric stimulation.