ABSTRACT
The mechanisms linking the brain's network structure to cognitively relevant activation patterns remain largely unknown. Here, by leveraging principles of network control, we show how the architecture of the human connectome shapes transitions between 123 experimentally defined cognitive activation maps (cognitive topographies) from the NeuroSynth meta-analytic database. Specifically, we systematically integrated large-scale multimodal neuroimaging data from functional magnetic resonance imaging, diffusion tractography, cortical morphometry and positron emission tomography to simulate how anatomically guided transitions between cognitive states can be reshaped by neurotransmitter engagement or by changes in cortical thickness. Our model incorporates neurotransmitter-receptor density maps (18 receptors and transporters) and maps of cortical thickness pertaining to a wide range of mental health, neurodegenerative, psychiatric and neurodevelopmental diagnostic categories (17,000 patients and 22,000 controls). The results provide a comprehensive look-up table charting how brain network organization and chemoarchitecture interact to manifest different cognitive topographies, and establish a principled foundation for the systematic identification of ways to promote selective transitions between cognitive topographies.
ABSTRACT
The macroscale connectome is the network of physical, white-matter tracts between brain areas. The connections are generally weighted and their values interpreted as measures of communication efficacy. In most applications, weights are either assigned based on imaging features-e.g. diffusion parameters-or inferred using statistical models. In reality, the ground-truth weights are unknown, motivating the exploration of alternative edge weighting schemes. Here, we explore a multi-modal, regression-based model that endows reconstructed fiber tracts with directed and signed weights. We find that the model fits observed data well, outperforming a suite of null models. The estimated weights are subject-specific and highly reliable, even when fit using relatively few training samples, and the networks maintain a number of desirable features. In summary, we offer a simple framework for weighting connectome data, demonstrating both its ease of implementation while benchmarking its utility for typical connectome analyses, including graph theoretic modeling and brain-behavior associations.
Subject(s)
Brain , Connectome , White Matter , Humans , Brain/diagnostic imaging , Brain/anatomy & histology , Brain/physiology , White Matter/diagnostic imaging , White Matter/anatomy & histology , White Matter/physiology , Male , Female , Adult , Models, Neurological , Nerve Net/physiology , Nerve Net/diagnostic imaging , Nerve Net/anatomy & histology , Diffusion Tensor Imaging/methods , Young Adult , Magnetic Resonance Imaging/methodsABSTRACT
Decades of neuroscience research has shown that macroscale brain dynamics can be reliably decomposed into a subset of large-scale functional networks, but the specific spatial topographies of these networks and the names used to describe them can vary across studies. Such discordance has hampered interpretation and convergence of research findings across the field. To address this problem, we have developed the Network Correspondence Toolbox (NCT) to permit researchers to examine and report spatial correspondence between their novel neuroimaging results and sixteen widely used functional brain atlases, consistent with recommended reporting standards developed by the Organization for Human Brain Mapping. The atlases included in the toolbox show some topographical convergence for specific networks, such as those labeled as default or visual. Network naming varies across atlases, particularly for networks spanning frontoparietal association cortices. For this reason, quantitative comparison with multiple atlases is recommended to benchmark novel neuroimaging findings. We provide several exemplar demonstrations using the Human Connectome Project task fMRI results and UK Biobank independent component analysis maps to illustrate how researchers can use the NCT to report their own findings through quantitative evaluation against multiple published atlases. The NCT provides a convenient means for computing Dice coefficients with spin test permutations to determine the magnitude and statistical significance of correspondence among user-defined maps and existing atlas labels. The NCT also includes functionality to incorporate additional atlases in the future. The adoption of the NCT will make it easier for network neuroscience researchers to report their findings in a standardized manner, thus aiding reproducibility and facilitating comparisons between studies to produce interdisciplinary insights.
ABSTRACT
Individual differences in neuroimaging are of interest to clinical and cognitive neuroscientists based on their potential for guiding the personalized treatment of various heterogeneous neurological conditions and diseases. Despite many advantages, the workhorse in this arena, BOLD (blood-oxygen-level-dependent) functional magnetic resonance imaging (fMRI) suffers from low spatiotemporal resolution and specificity as well as a propensity for noise and spurious signal corruption. To better understand individual differences in BOLD-fMRI data, we can use animal models where fMRI, alongside complementary but more invasive contrasts, can be accessed. Here, we apply simultaneous wide-field fluorescence calcium imaging and BOLD-fMRI in mice to interrogate individual differences using a connectome-based identification framework adopted from the human fMRI literature. This approach yields high spatiotemporal resolution cell-type specific signals (here, from glia, excitatory, as well as inhibitory interneurons) from the whole cortex. We found mouse multimodal connectome- based identification to be successful and explored various features of these data.
ABSTRACT
It is commonplace in neuroscience to assume that if two tasks activate the same brain areas in the same way, then they are recruiting the same underlying networks. Yet computational theory has shown that the same pattern of activity can emerge from many different underlying network representations. Here we evaluated whether similarity in activation necessarily implies similarity in network architecture by comparing region-wise activation patterns and functional correlation profiles from a large sample of healthy subjects (N = 242). Participants performed two executive control tasks known to recruit nearly identical brain areas, the color-word Stroop task and the Multi-Source Interference Task (MSIT). Using a measure of instantaneous functional correlations, based on edge time series, we estimated the task-related networks that differed between incongruent and congruent conditions. We found that the two tasks were much more different in their network profiles than in their evoked activity patterns at different analytical levels, as well as for a wide range of methodological pipelines. Our results reject the notion that having the same activation patterns means two tasks engage the same underlying representations, suggesting that task representations should be independently evaluated at both node and edge (connectivity) levels.
As a dynamical system, the brain can encode information at the module (e.g., brain regions) or the network level (e.g., connections between brain regions). This means that two tasks can produce the same pattern of activation, but differ in their network profile. Here we tested this using two tasks with largely similar cognitive requirements. Despite producing nearly identical macroscopic activation patterns, the two tasks produced different functional network profiles. These findings confirm prior theoretical work that similarity in task activation does not imply the same similarity in underlying network states.
ABSTRACT
Decreased neuronal specificity of the brain in response to cognitive demands (i.e., neural dedifferentiation) has been implicated in age-related cognitive decline. Investigations into functional connectivity analogs of these processes have focused primarily on measuring segregation of nonoverlapping networks at rest. Here, we used an edge-centric network approach to derive entropy, a measure of specialization, from spatially overlapping communities during cognitive task fMRI. Using Human Connectome Project Lifespan data (713 participants, 36-100â years old, 55.7% female), we characterized a pattern of nodal despecialization differentially affecting the medial temporal lobe and limbic, visual, and subcortical systems. At the whole-brain level, global entropy moderated declines in fluid cognition across the lifespan and uniquely covaried with age when controlling for the network segregation metric modularity. Importantly, relationships between both metrics (entropy and modularity) and fluid cognition were age dependent, although entropy's relationship with cognition was specific to older adults. These results suggest entropy is a potentially important metric for examining how neurological processes in aging affect functional specialization at the nodal, network, and whole-brain level.
Subject(s)
Aging , Brain , Cognition , Connectome , Entropy , Magnetic Resonance Imaging , Nerve Net , Humans , Female , Male , Aged , Middle Aged , Adult , Aging/physiology , Aging/psychology , Cognition/physiology , Aged, 80 and over , Brain/physiology , Brain/diagnostic imaging , Nerve Net/physiology , Nerve Net/diagnostic imagingABSTRACT
The human brain is never at "rest"; its activity is constantly fluctuating over time, transitioning from one brain state-a whole-brain pattern of activity-to another. Network control theory offers a framework for understanding the effort - energy - associated with these transitions. One branch of control theory that is especially useful in this context is "optimal control", in which input signals are used to selectively drive the brain into a target state. Typically, these inputs are introduced independently to the nodes of the network (each input signal is associated with exactly one node). Though convenient, this input strategy ignores the continuity of cerebral cortex - geometrically, each region is connected to its spatial neighbors, allowing control signals, both exogenous and endogenous, to spread from their foci to nearby regions. Additionally, the spatial specificity of brain stimulation techniques is limited, such that the effects of a perturbation are measurable in tissue surrounding the stimulation site. Here, we adapt the network control model so that input signals have a spatial extent that decays exponentially from the input site. We show that this more realistic strategy takes advantage of spatial dependencies in structural connectivity and activity to reduce the energy (effort) associated with brain state transitions. We further leverage these dependencies to explore near-optimal control strategies such that, on a per-transition basis, the number of input signals required for a given control task is reduced, in some cases by two orders of magnitude. This approximation yields network-wide maps of input site density, which we compare to an existing database of functional, metabolic, genetic, and neurochemical maps, finding a close correspondence. Ultimately, not only do we propose a more efficient framework that is also more adherent to well-established brain organizational principles, but we also posit neurobiologically grounded bases for optimal control.
ABSTRACT
Connectome generative models, otherwise known as generative network models, provide insight into the wiring principles underpinning brain network organization. While these models can approximate numerous statistical properties of empirical networks, they typically fail to explicitly characterize an important contributor to brain organization - axonal growth. Emulating the chemoaffinity guided axonal growth, we provide a novel generative model in which axons dynamically steer the direction of propagation based on distance-dependent chemoattractive forces acting on their growth cones. This simple dynamic growth mechanism, despite being solely geometry-dependent, is shown to generate axonal fiber bundles with brain-like geometry and features of complex network architecture consistent with the human brain, including lognormally distributed connectivity weights, scale-free nodal degrees, small-worldness, and modularity. We demonstrate that our model parameters can be fitted to individual connectomes, enabling connectome dimensionality reduction and comparison of parameters between groups. Our work offers an opportunity to bridge studies of axon guidance and connectome development, providing new avenues for understanding neural development from a computational perspective.
ABSTRACT
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.
Subject(s)
Connectome , Animals , Connectome/methods , Brain , Mammals , Databases, Factual , Communication , Nerve NetABSTRACT
Background: Properties of functional connectivity (FC), such as network integration and segregation, are shown to be associated with various human behaviors. For example, Godwin et al. and Sun et al. found increased integration with attention allocation, whereas Cohen and D'Esposito and Shine et al. observed increased segregation with simple motor tasks. The current study investigated how viewing video clips with different valence and arousal influenced integration-segregation properties in task-based FC networks. Methods: We analyzed an open dataset collected by Kim et al. We performed a generalized psychophysiological interaction (gPPI) analysis paired with network analysis and community detection to investigate changes in brain network dynamics when people watched four types of videos that differed by affective valence (unpleasant or pleasant) and arousal (arousing or calm). Results: Results showed that unpleasant arousing videos produced greater FC deviation from the baseline (task-induced FC deviation [tiFCd]) and perturbed the brain into a more segregated state than other kinds of video. Increased segregation was only observed in association systems, not sensorimotor systems. Discussion: Unpleasant arousing content perturbed the brain to a functionally distinct state from the other three types of affective videos. We suggest that the change in brain state was related to people disengaging from the unpleasant arousing content or, alternatively, staying alert while exposed to unpleasant arousing stimuli. The study also added to our understanding of how combining task-based gPPI analysis with community detection methods and network segregation measures can advance our knowledge of the links between behavior and brain state changes. Impact statement Network integration and segregation is an important property of the human brain. We address the question of how affective stimuli influence brain dynamics from a functional connectivity (FC) network integration-segregation perspective. By conducting a whole-brain generalized psychophysiological interaction (gPPI) analysis paired with community detection methods, we found that highly aversive video content induced significant FC changes and perturbed the brain to a more segregated state.
Subject(s)
Brain , Magnetic Resonance Imaging , Humans , Brain/physiology , Wakefulness , Emotions/physiology , Attention/physiology , Brain Mapping/methodsABSTRACT
Previous studies have adopted an edge-centric framework to study fine-scale network dynamics in human fMRI. To date, however, no studies have applied this framework to data collected from model organisms. Here, we analyze structural and functional imaging data from lightly anesthetized mice through an edge-centric lens. We find evidence of "bursty" dynamics and events - brief periods of high-amplitude network connectivity. Further, we show that on a per-frame basis events best explain static FC and can be divided into a series of hierarchically-related clusters. The co-fluctuation patterns associated with each cluster centroid link distinct anatomical areas and largely adhere to the boundaries of algorithmically detected functional brain systems. We then investigate the anatomical connectivity undergirding high-amplitude co-fluctuation patterns. We find that events induce modular bipartitions of the anatomical network of inter-areal axonal projections. Finally, we replicate these same findings in a human imaging dataset. In summary, this report recapitulates in a model organism many of the same phenomena observed in previously edge-centric analyses of human imaging data. However, unlike human subjects, the murine nervous system is amenable to invasive experimental perturbations. Thus, this study sets the stage for future investigation into the causal origins of fine-scale brain dynamics and high-amplitude co-fluctuations. Moreover, the cross-species consistency of the reported findings enhances the likelihood of future translation.
Subject(s)
Araceae , Connectome , Lens, Crystalline , Humans , Animals , Mice , Brain/diagnostic imaging , AxonsABSTRACT
Understanding the interrelationships of brain function as measured by resting-state magnetic resonance imaging and neuropsychological/behavioral measures in Alzheimer's disease is key for advancement of neuroimaging analysis methods in clinical research. The edge time-series framework recently developed in the field of network neuroscience, in combination with other network science methods, allows for investigations of brain-behavior relationships that are not possible with conventional functional connectivity methods. Data from the Indiana Alzheimer's Disease Research Center sample (53 cognitively normal control, 47 subjective cognitive decline, 32 mild cognitive impairment, and 20 Alzheimer's disease participants) were used to investigate relationships between functional connectivity components, each derived from a subset of time points based on co-fluctuation of regional signals, and measures of domain-specific neuropsychological functions. Multiple relationships were identified with the component approach that were not found with conventional functional connectivity. These involved attentional, limbic, frontoparietal, and default mode systems and their interactions, which were shown to couple with cognitive, executive, language, and attention neuropsychological domains. Additionally, overlapping results were obtained with two different statistical strategies (network contingency correlation analysis and network-based statistics correlation). Results demonstrate that connectivity components derived from edge time-series based on co-fluctuation reveal disease-relevant relationships not observed with conventional static functional connectivity.
Subject(s)
Alzheimer Disease , Cognitive Dysfunction , Humans , Alzheimer Disease/pathology , Time Factors , Magnetic Resonance Imaging , Brain , Cognition , Nerve NetABSTRACT
Memory consolidation occurs via reactivation of a hippocampal index during non-rapid eye movement slow-wave sleep (NREM SWS) which binds attributes of an experience existing within cortical modules. For memories containing emotional content, hippocampal-amygdala dynamics facilitate consolidation over a sleep bout. This study tested if modularity and centrality-graph theoretical measures that index the level of segregation/integration in a system and the relative import of its nodes-map onto central tenets of memory consolidation theory and sleep-related processing. Findings indicate that greater network integration is tied to overnight emotional memory retention via NREM SWS expression. Greater hippocampal and amygdala influence over network organization supports emotional memory retention, and hippocampal or amygdala control over information flow are differentially associated with distinct stages of memory processing. These centrality measures are also tied to the local expression and coupling of key sleep oscillations tied to sleep-dependent memory consolidation. These findings suggest that measures of intrinsic network connectivity may predict the capacity of brain functional networks to acquire, consolidate, and retrieve emotional memories.
ABSTRACT
Hub regions in the brain, recognized for their roles in ensuring efficient information transfer, are vulnerable to pathological alterations in neurodegenerative conditions, including Alzheimer Disease (AD). Given their essential role in neural communication, disruptions to these hubs have profound implications for overall brain network integrity and functionality. Hub disruption, or targeted impairment of functional connectivity at the hubs, is recognized in AD patients. Computational models paired with evidence from animal experiments hint at a mechanistic explanation, suggesting that these hubs may be preferentially targeted in neurodegeneration, due to their high neuronal activity levels-a phenomenon termed "activity-dependent degeneration". Yet, two critical issues were unresolved. First, past research hasn't definitively shown whether hub regions face a higher likelihood of impairment (targeted attack) compared to other regions or if impairment likelihood is uniformly distributed (random attack). Second, human studies offering support for activity-dependent explanations remain scarce. We applied a refined hub disruption index to determine the presence of targeted attacks in AD. Furthermore, we explored potential evidence for activity-dependent degeneration by evaluating if hub vulnerability is better explained by global connectivity or connectivity variations across functional systems, as well as comparing its timing relative to amyloid beta deposition in the brain. Our unique cohort of participants with autosomal dominant Alzheimer Disease (ADAD) allowed us to probe into the preclinical stages of AD to determine the hub disruption timeline in relation to expected symptom emergence. Our findings reveal a hub disruption pattern in ADAD aligned with targeted attacks, detectable even in pre-clinical stages. Notably, the disruption's severity amplified alongside symptomatic progression. Moreover, since excessive local neuronal activity has been shown to increase amyloid deposition and high connectivity regions show high level of neuronal activity, our observation that hub disruption was primarily tied to regional differences in global connectivity and sequentially followed changes observed in Aß PET cortical markers is consistent with the activity-dependent degeneration model. Intriguingly, these disruptions were discernible 8 years before the expected age of symptom onset. Taken together, our findings not only align with the targeted attack on hubs model but also suggest that activity-dependent degeneration might be the cause of hub vulnerability. This deepened understanding could be instrumental in refining diagnostic techniques and developing targeted therapeutic strategies for AD in the future.
ABSTRACT
Understanding the interrelationships of brain function as measured by resting-state magnetic resonance imaging and neuropsychological/behavioral measures in Alzheimer's disease is key for advancement of neuroimaging analysis methods in clinical research. The edge time-series framework recently developed in the field of network neuroscience, in combination with other network science methods, allows for investigations of brain-behavior relationships that are not possible with conventional functional connectivity methods. Data from the Indiana Alzheimer's Disease Research Center sample (53 cognitively normal control, 47 subjective cognitive decline, 32 mild cognitive impairment, and 20 Alzheimer's disease participants) were used to investigate relationships between functional connectivity components, each derived from a subset of time points based on co-fluctuation of regional signals, and measures of domain-specific neuropsychological functions. Multiple relationships were identified with the component approach that were not found with conventional functional connectivity. These involved attentional, limbic, frontoparietal, and default mode systems and their interactions, which were shown to couple with cognitive, executive, language, and attention neuropsychological domains. Additionally, overlapping results were obtained with two different statistical strategies (network contingency correlation analysis and network-based statistics correlation). Results demonstrate that connectivity components derived from edge time-series based on co-fluctuation reveal disease-relevant relationships not observed with conventional static functional connectivity.
ABSTRACT
Progress in scientific disciplines is accompanied by standardization of terminology. Network neuroscience, at the level of macroscale organization of the brain, is beginning to confront the challenges associated with developing a taxonomy of its fundamental explanatory constructs. The Workgroup for HArmonized Taxonomy of NETworks (WHATNET) was formed in 2020 as an Organization for Human Brain Mapping (OHBM)-endorsed best practices committee to provide recommendations on points of consensus, identify open questions, and highlight areas of ongoing debate in the service of moving the field toward standardized reporting of network neuroscience results. The committee conducted a survey to catalog current practices in large-scale brain network nomenclature. A few well-known network names (e.g., default mode network) dominated responses to the survey, and a number of illuminating points of disagreement emerged. We summarize survey results and provide initial considerations and recommendations from the workgroup. This perspective piece includes a selective review of challenges to this enterprise, including (1) network scale, resolution, and hierarchies; (2) interindividual variability of networks; (3) dynamics and nonstationarity of networks; (4) consideration of network affiliations of subcortical structures; and (5) consideration of multimodal information. We close with minimal reporting guidelines for the cognitive and network neuroscience communities to adopt.
ABSTRACT
A rapidly emerging application of network neuroscience in neuroimaging studies has provided useful tools to understand individual differences in intrinsic brain function by mapping spontaneous brain activity, namely intrinsic functional network neuroscience (ifNN). However, the variability of methodologies applied across the ifNN studies-with respect to node definition, edge construction, and graph measurements-makes it difficult to directly compare findings and also challenging for end users to select the optimal strategies for mapping individual differences in brain networks. Here, we aim to provide a benchmark for best ifNN practices by systematically comparing the measurement reliability of individual differences under different ifNN analytical strategies using the test-retest design of the Human Connectome Project. The results uncovered four essential principles to guide ifNN studies: (1) use a whole brain parcellation to define network nodes, including subcortical and cerebellar regions; (2) construct functional networks using spontaneous brain activity in multiple slow bands; and (3) optimize topological economy of networks at individual level; and (4) characterize information flow with specific metrics of integration and segregation. We built an interactive online resource of reliability assessments for future ifNN (https://ibraindata.com/research/ifNN).
ABSTRACT
Edge time series decompose functional connectivity into its framewise contributions. Previous studies have focused on characterizing the properties of high-amplitude frames (time points when the global co-fluctuation amplitude takes on its largest value), including their cluster structure. Less is known about middle- and low-amplitude co-fluctuations (peaks in co-fluctuation time series but of lower amplitude). Here, we directly address those questions, using data from two dense-sampling studies: the MyConnectome project and Midnight Scan Club. We develop a hierarchical clustering algorithm to group peak co-fluctuations of all magnitudes into nested and multiscale clusters based on their pairwise concordance. At a coarse scale, we find evidence of three large clusters that, collectively, engage virtually all canonical brain systems. At finer scales, however, each cluster is dissolved, giving way to increasingly refined patterns of co-fluctuations involving specific sets of brain systems. We also find an increase in global co-fluctuation magnitude with hierarchical scale. Finally, we comment on the amount of data needed to estimate co-fluctuation pattern clusters and implications for brain-behavior studies. Collectively, the findings reported here fill several gaps in current knowledge concerning the heterogeneity and richness of co-fluctuation patterns as estimated with edge time series while providing some practical guidance for future studies.
ABSTRACT
Many studies have shown that the human endocrine system modulates brain function, reporting associations between fluctuations in hormone concentrations and brain connectivity. However, how hormonal fluctuations impact fast changes in brain network organization over short timescales remains unknown. Here, we leverage a recently proposed framework for modeling co-fluctuations between the activity of pairs of brain regions at a framewise timescale. In previous studies we showed that time points corresponding to high-amplitude co-fluctuations disproportionately contributed to the time-averaged functional connectivity pattern and that these co-fluctuation patterns could be clustered into a low-dimensional set of recurring "states." Here, we assessed the relationship between these network states and quotidian variation in hormone concentrations. Specifically, we were interested in whether the frequency with which network states occurred was related to hormone concentration. We addressed this question using a dense-sampling dataset (N = 1 brain). In this dataset, a single individual was sampled over the course of two endocrine states: a natural menstrual cycle and while the subject underwent selective progesterone suppression via oral hormonal contraceptives. During each cycle, the subject underwent 30 daily resting-state fMRI scans and blood draws. Our analysis of the imaging data revealed two repeating network states. We found that the frequency with which state 1 occurred in scan sessions was significantly correlated with follicle-stimulating and luteinizing hormone concentrations. We also constructed representative networks for each scan session using only "event frames"-those time points when an event was determined to have occurred. We found that the weights of specific subsets of functional connections were robustly correlated with fluctuations in the concentration of not only luteinizing and follicle-stimulating hormones, but also progesterone and estradiol.
ABSTRACT
Network neuroscience has emphasized the connectional properties of neural elements - cells, populations, and regions. This has come at the expense of the anatomical and functional connections that link these elements to one another. A new perspective - namely one that emphasizes 'edges' - may prove fruitful in addressing outstanding questions in network neuroscience. We highlight one recently proposed 'edge-centric' method and review its current applications, merits, and limitations. We also seek to establish conceptual and mathematical links between this method and previously proposed approaches in the network science and neuroimaging literature. We conclude by presenting several avenues for future work to extend and refine existing edge-centric analysis.