Network neuroscience has relied on a node-centric network model in which cells, populations and regions are linked to one another via anatomical or functional connections. This model cannot account for interactions of edges with one another. In this study, we developed an edge-centric network model that generates constructs ‘edge time series’ and ‘edge functional connectivity’ (eFC). Using network analysis, we show that, at rest, eFC is consistent across datasets and reproducible within the same individual over multiple scan sessions. We demonstrate that clustering eFC yields communities of edges that naturally divide the brain into overlapping clusters, with regions in sensorimotor and attentional networks exhibiting the greatest levels of overlap. We show that eFC is systematically modulated by variation in sensory input. In future work, the edge-centric approach could be useful for identifying novel biomarkers of disease, characterizing individual variation and mapping the architecture of highly resolved neural circuits.
Subscribe to Journal
Get full journal access for 1 year
only $17.42 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
All imaging data come from publicly available, open access repositories. Human Connectome Project data can be accessed at https://db.humanconnectome.org/app/template/Login.vm after signing a data use agreement. Midnight Scan Club data can be accessed via OpenNeuro at https://openneuro.org/datasets/ds000224/versions/1.0.1. The Healthy Brain Network Serial Scanning Initiative data can be accessed at https://fcon_1000.projects.nitrc.org/indi/hbn_ssi/download.html.
Code to compute eFC and its related derivatives has been made available at https://github.com/brain-networks.
Bassett, D. S. & Sporns, O. Network neuroscience. Nat. Neurosci. 20, 353–364 (2017).
Schröter, M., Paulsen, O. & Bullmore, E. T. Micro-connectomics: probing the organization of neuronal networks at the cellular scale. Nat. Rev. Neurosci. 18, 131–146 (2017).
Dann, B., Michaels, J. A., Schaffelhofer, S. & Scherberger, H. Uniting functional network topology and oscillations in the fronto-parietal single unit network of behaving primates. eLife 5, e15719 (2016).
Park, H.-J. & Friston, K. Structural and functional brain networks: from connections to cognition. Science 342, 1238411 (2013).
Sporns, O. & Zwi, J. D. The small world of the cerebral cortex. Neuroinformatics 2, 145–162 (2004).
Power, J. D., Schlaggar, B. L., Lessov-Schlaggar, C. N. & Petersen, S. E. Evidence for hubs in human functional brain networks. Neuron 79, 798–813 (2013).
Sporns, O. & Betzel, R. F. Modular brain networks. Annu. Rev. Psychol. 67, 613–640 (2016).
Bullmore, E. & Sporns, O. The economy of brain network organization. Nat. Rev. Neurosci. 13, 336–349 (2012).
Bullmore, E. & Sporns, O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186–198 (2009).
Rubinov, M. & Sporns, O. Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059–1069 (2010).
Ahn, Y.-Y., Bagrow, J. P. & Lehmann, S. Link communities reveal multiscale complexity in networks. Nature 466, 761–764 (2010).
Evans, T. & Lambiotte, R. Line graphs, link partitions, and overlapping communities. Phys. Rev. E 80, 016105 (2009).
Eickhoff, S. B., Constable, R. T. & Yeo, B. T. Topographic organization of the cerebral cortex and brain cartography. Neuroimage 170, 332–347 (2018).
de Reus, M. A., Saenger, V. M., Kahn, R. S. & van den Heuvel, M. P. An edge-centric perspective on the human connectome: link communities in the brain. Philos. Trans. R. Soc. B Biol. Sci. 369, 20130527 (2014).
Smith, S. M. et al. Network modelling methods for FMRI. Neuroimage 54, 875–891 (2011).
Reid, A. T. et al. Advancing functional connectivity research from association to causation. Nat. Neurosci. 22, 1751–1760 (2019).
Van Essen, D. C. et al. The WU-Minn Human Connectome Project: an overview. Neuroimage 80, 62–79 (2013).
Gordon, E. M. et al. Precision functional mapping of individual human brains. Neuron 95, 791–807 (2017).
O’Connor, D. et al. The healthy brain network serial scanning initiative: a resource for evaluating inter-individual differences and their reliabilities across scan conditions and sessions. Gigascience 6, giw011 (2017).
van Oort, E. S. et al. Functional parcellation using time courses of instantaneous connectivity. Neuroimage 170, 31–40 (2018).
Esfahlani, F. Z., Bertolero, M. A., Bassett, D. S. & Betzel, R. F. Space-independent community and hub structure of functional brain networks. Neuroimage 211, 116612 (2020).
Schaefer, A. et al. Local–global parcellation of the human cerebral cortex from intrinsic functional connectivity MRI. Cereb. Cortex 28, 3095–3114 (2018).
Laumann, T. O. et al. Functional system and areal organization of a highly sampled individual human brain. Neuron 87, 657–670 (2015).
Amico, E. & Goñi, J. The quest for identifiability in human functional connectomes. Sci. Rep. 8, 8254 (2018).
Bassett, D. S. et al. Dynamic reconfiguration of human brain networks during learning. Proc. Natl Acad. Sci. USA 108, 7641–7646 (2011).
Finn, E. S. et al. Functional connectome fingerprinting: identifying individuals using patterns of brain connectivity. Nat. Neurosci. 18, 1664–1671 (2015).
Anderson, M. L., Kinnison, J. & Pessoa, L. Describing functional diversity of brain regions and brain networks. Neuroimage 73, 50–58 (2013).
Pessoa, L. Understanding brain networks and brain organization. Phys. Life Rev. 11, 400–435 (2014).
Yeo, B. T., Krienen, F. M., Chee, M. W. & Buckner, R. L. Estimates of segregation and overlap of functional connectivity networks in the human cerebral cortex. Neuroimage 88, 212–227 (2014).
Wilf, M. et al. Spontaneously emerging patterns in human visual cortex reflect responses to naturalistic sensory stimuli. Cereb. Cortex 27, 750–763 (2017).
Baldassano, C., Hasson, U. & Norman, K. A. Representation of real-world event schemas during narrative perception. J. Neurosci. 38, 9689–9699 (2018).
Avena-Koenigsberger, A., Misic, B. & Sporns, O. Communication dynamics in complex brain networks. Nat. Rev. Neurosci. 19, 17 (2018).
Shine, J. M. et al. Estimation of dynamic functional connectivity using multiplication of temporal derivatives. Neuroimage 122, 399–407 (2015).
Liu, X. & Duyn, J. H. Time-varying functional network information extracted from brief instances of spontaneous brain activity. Proc. Natl Acad. Sci. USA 110, 4392–4397 (2013).
Newman, M. E. & Girvan, M. Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004).
Rosvall, M. & Bergstrom, C. T. Maps of random walks on complex networks reveal community structure. Proc. Natl Acad. Sci. USA 105, 1118–1123 (2008).
Bertolero, M. A., Yeo, B. T. & D’Esposito, M. The modular and integrative functional architecture of the human brain. Proc. Natl Acad. Sci. USA 112, E6798–E6807 (2015).
Smith, S. M. et al. Correspondence of the brain’s functional architecture during activation and rest. Proc. Natl Acad. Sci. USA 106, 13040–13045 (2009).
Cole, M. W. et al. Task activations produce spurious but systematic inflation of task functional connectivity estimates. Neuroimage 189, 1–18 (2019).
Margulies, D. S. et al. Situating the default-mode network along a principal gradient of macroscale cortical organization. Proc. Natl Acad. Sci. USA 113, 12574–12579 (2016).
Esfahlani, F. Z. et al. High-amplitude co-fluctuations in cortical activity drive functional connectivity. Preprint at bioRxiv https://doi.org/10.1101/800045 (2020).
Lurie, D. J. et al. Questions and controversies in the study of time-varying functional connectivity in resting fMRI. Netw. Neurosci. 4, 30–69 (2020).
King, M., Hernandez-Castillo, C. R., Poldrack, R. A., Ivry, R. B. & Diedrichsen, J. Functional boundaries in the human cerebellum revealed by a multi-domain task battery. Nat. Neurosci. 22, 1371–1378 (2019).
Pereira, F., Mitchell, T. & Botvinick, M. Machine learning classifiers and fMRI: a tutorial overview. Neuroimage 45, S199–S209 (2009).
Huys, Q. J., Maia, T. V. & Frank, M. J. Computational psychiatry as a bridge from neuroscience to clinical applications. Nat. Neurosci. 19, 404 (2016).
McIntosh, A. R. & Mišić, B. Multivariate statistical analyses for neuroimaging data. Annu. Rev. Psychol. 64, 499–525 (2013).
Zalesky, A., Fornito, A. & Bullmore, E. On the use of correlation as a measure of network connectivity. Neuroimage 60, 2096–2106 (2012).
Owen, L. L., Chang, T. H. & Manning, J. R. High-level cognition during story listening is reflected in high-order dynamic correlations in neural activity patterns. Preprint at bioRxiv https://doi.org/10.1101/763821 (2019).
Sizemore, A. E., Phillips-Cremins, J. E., Ghrist, R. & Bassett, D. S. The importance of the whole: topological data analysis for the network neuroscientist. Netw. Neurosci. 3, 656–673 (2019).
Khambhati, A. N. et al. Dynamic network drivers of seizure generation, propagation and termination in human neocortical epilepsy. PLoS Comput. Biol. 11, e1004608 (2015).
Shine, J. M. et al. Human cognition involves the dynamic integration of neural activity and neuromodulatory systems. Nat. Neurosci. 22, 289–296 (2019).
Davison, E. N. et al. Brain network adaptability across task states. PLoS Comput. Biol. 11, e1004029 (2015).
Glasser, M. F. et al. The minimal preprocessing pipelines for the Human Connectome Project. Neuroimage 80, 105–124 (2013).
Robinson, E. C. et al. MSM: a new flexible framework for multimodal surface matching. Neuroimage 100, 414–426 (2014).
Esteban, O. et al. fMRIPrep: a robust preprocessing pipeline for functional MRI. Nat. Methods 16, 111–116 (2019).
Gorgolewski, K. et al. Nipype: a flexible, lightweight and extensible neuroimaging data processing framework in Python. Front. Neuroinform. 5, 13 (2011).
Abraham, A. et al. Machine learning for neuroimaging with scikit-learn. Front. Neuroinform. 8, 14 (2014).
Avants, B. B., Epstein, C. L., Grossman, M. & Gee, J. C. Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain. Med. Image Anal. 12, 26–41 (2008).
Tustison, N. J. et al. N4ITK: improved N3 bias correction. IEEE Trans. Med. Imaging 29, 1310–1320 (2010).
Dale, A. M., Fischl, B. & Sereno, M. I. Cortical surface-based analysis: I. Segmentation and surface reconstruction. Neuroimage 9, 179–194 (1999).
Klein, A. et al. Mindboggling morphometry of human brains. PLoS Comput. Biol. 13, e1005350 (2017).
Fonov, V. S., Evans, A. C., McKinstry, R. C., Almli, C. & Collins, D. Unbiased nonlinear average age-appropriate brain templates from birth to adulthood. Neuroimage 47, S102 (2009).
Zhang, Y., Brady, M. & Smith, S. Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm. IEEE Trans. Med. Imaging 20, 45–57 (2001).
Jenkinson, M., Bannister, P., Brady, M. & Smith, S. Improved optimization for the robust and accurate linear registration and motion correction of brain images. Neuroimage 17, 825–841 (2002).
Wang, S. et al. Evaluation of field map and nonlinear registration methods for correction of susceptibility artifacts in diffusion MRI. Front. Neuroinform. 11, 17 (2017).
Treiber, J. M. et al. Characterization and correction of geometric distortions in 814 diffusion weighted images. PLoS ONE 11, e0152472 (2016).
Greve, D. N. & Fischl, B. Accurate and robust brain image alignment using boundary-based registration. Neuroimage 48, 63–72 (2009).
Power, J. D. et al. Methods to detect, characterize, and remove motion artifact in resting state fMRI. Neuroimage 84, 320–341 (2014).
Esteban, O. et al. MRIQC: advancing the automatic prediction of image quality in MRI from unseen sites. PLoS ONE 12, e0184661 (2017).
Parkes, L., Fulcher, B., Yücel, M. & Fornito, A. An evaluation of the efficacy, reliability, and sensitivity of motion correction strategies for resting-state functional MRI. Neuroimage 171, 415–436 (2018).
Yeo, B. T. et al. The organization of the human cerebral cortex estimated by intrinsic functional connectivity. J. Neurophysiol. 106, 1126–1165 (2011).
Fischl, B. et al. Automatically parcellating the human cerebral cortex. Cereb. Cortex 14, 11–22 (2004).
Lindquist, M. A., Geuter, S., Wager, T. D. & Caffo, B. S. Modular preprocessing pipelines can reintroduce artifacts into fMRI data. Hum. Brain Mapp. 40, 2358–2376 (2019).
Satterthwaite, T. D. et al. An improved framework for confound regression and filtering for control of motion artifact in the preprocessing of resting-state functional connectivity data. Neuroimage 64, 240–256 (2013).
Gopalan, P. K. & Blei, D. M. Efficient discovery of overlapping communities in massive networks. Proc. Natl Acad. Sci. USA 110, 14534–14539 (2013).
Yang, J. & Leskovec, J. Overlapping communities explain core-periphery organization of networks. Proc. IEEE 102, 1892–1902 (2014).
Psorakis, I., Roberts, S., Ebden, M. & Sheldon, B. Overlapping community detection using Bayesian non-negative matrix factorization. Phys. Rev. E 83, 066114 (2011).
Najafi, M., McMenamin, B. W., Simon, J. Z. & Pessoa, L. Overlapping communities reveal rich structure in large-scale brain networks during rest and task conditions. Neuroimage 135, 92–106 (2016).
Guimera, R. & Amaral, L. A. N. Functional cartography of complex metabolic networks. Nature 433, 895–900 (2005).
Shinn, M. et al. Versatility of nodal affiliation to communities. Sci. Rep. 7, 1–10 (2017).
Pedersen, M., Zalesky, A., Omidvarnia, A. & Jackson, G. D. Multilayer network switching rate predicts brain performance. Proc. Natl Acad. Sci. USA 115, 13376–13381 (2018).
Reichardt, J. & Bornholdt, S. Statistical mechanics of community detection. Phys. Rev. E 74, 016110 (2006).
Traag, V. A., Van Dooren, P. & Nesterov, Y. Narrow scope for resolution-limit-free community detection. Phys. Rev. E 84, 016114 (2011).
Bazzi, M. et al. Community detection in temporal multilayer networks, with an application to correlation networks. Multiscale Model. Simul. 14, 1–41 (2016).
Betzel, R. F. et al. The community structure of functional brain networks exhibits scale-specific patterns of inter-and intra-subject variability. Neuroimage 202, 115990 (2019).
Mucha, P. J., Richardson, T., Macon, K., Porter, M. A. & Onnela, J.-P. Community structure in time-dependent, multiscale, and multiplex networks. Science 328, 876–878 (2010).
Smith, S. M. et al. A positive–negative mode of population covariation links brain connectivity, demographics and behavior. Nat. Neurosci. 18, 1565–1567 (2015).
This research was supported by the Indiana University Office of the Vice President for Research Emerging Area of Research Initiative, Learning: Brains, Machines and Children (F.Z.E. and R.F.B.). This material is based on work supported by the National Science Foundation Graduate Research Fellowship under grant no. 1342962 (J.F.). This research was supported, in part, by the Lilly Endowment, through its support for the Indiana University Pervasive Technology Institute and, in part, by the Indiana METACyt Initiative. The Indiana METACyt Initiative at Indiana University was also supported, in part, by the Lilly Endowment. Data were provided, in part, by the Human Connectome Project, WU-Minn Consortium (principal investigators: D. Van Essen and K. Ugurbil; 1U54MH091657), funded by the 16 National Institues of Health (NIH) institutes and centers that support the NIH Blueprint for Neuroscience Research and by the McDonnell Center for Systems Neuroscience at Washington University. We thank B. Mišić for reading an early version of this manuscript.
The authors declare no competing interests.
Peer review information Nature Neuroscience thanks Lucina Uddin, Andrew Zalesky, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Faskowitz, J., Esfahlani, F.Z., Jo, Y. et al. Edge-centric functional network representations of human cerebral cortex reveal overlapping system-level architecture. Nat Neurosci 23, 1644–1654 (2020). https://doi.org/10.1038/s41593-020-00719-y
Nature Neuroscience (2020)