Communication dynamics in complex brain networks

Article metrics

Key Points

  • The topology of structural brain networks shapes patterns of interaction and signalling among neurons and brain regions, and the resulting communication dynamics is important for brain function.

  • Different aspects of network topology imply different communication mechanisms, from routing of information through shortest paths to alternative models that involve spreading, diffusion and broadcasting.

  • Different topological attributes promote different types of communication mechanisms.

  • Communication dynamics are subject to competing constraints and demands (trade-offs) among efficiency, cost, versatility and resilience. One aspect of cost is the amount of information needed to implement network communication. This cost is high for routing and low for diffusion, and is likely to be an important factor for determining the biological feasibility of a given communication model.


Neuronal signalling and communication underpin virtually all aspects of brain activity and function. Network science approaches to modelling and analysing the dynamics of communication on networks have proved useful for simulating functional brain connectivity and predicting emergent network states. This Review surveys important aspects of communication dynamics in brain networks. We begin by sketching a conceptual framework that views communication dynamics as a necessary link between the empirical domains of structural and functional connectivity. We then consider how different local and global topological attributes of structural networks support potential patterns of network communication, and how the interactions between network topology and dynamic models can provide additional insights and constraints. We end by proposing that communication dynamics may act as potential generative models of effective connectivity and can offer insight into the mechanisms by which brain networks transform and process information.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: A conceptual framework for linking structural connectivity and functional connectivity.
Figure 2: Network topology and communication.
Figure 3: Interplay between architecture and communication dynamics.
Figure 4: Communication processes as a function of time.


  1. 1

    Laughlin, S. B. & Sejnowski, T. J. Communication in neuronal networks. Science 301, 1870–1874 (2003). This is an early (pre-connectomics) account that highlights the importance of economy and efficiency in network communication.

  2. 2

    Turk-Browne, N. B. Functional interactions as big data in the human brain. Science 342, 580–584 (2013).

  3. 3

    Sporns, O. Contributions and challenges for network models in cognitive neuroscience. Nat. Neurosci. 17, 652–660 (2014).

  4. 4

    Bullmore, E. & Sporns, O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186–198 (2009).

  5. 5

    Park, H. J. & Friston, K. Structural and functional brain networks: from connections to cognition. Science 342, 1238411–1238411 (2013).

  6. 6

    Petersen, S. E. & Sporns, O. Brain networks and cognitive architectures. Neuron 88, 207–219 (2015).

  7. 7

    Medaglia, J. D., Lynall, M.-E. & Bassett, D. S. Cognitive network neuroscience. J. Cogn. Neurosci. 27, 1471–1491 (2015).

  8. 8

    Roland, P. E., Hilgetag, C. C. & Deco, G. Cortico-cortical communication dynamics. Front. Syst. Neurosci. 8, 9 (2014).

  9. 9

    Newman, M., Barabási, A.-L. & Watts, D. J. The Structure and Dynamics of Networks. (Princeton Univ. Press, 2011).

  10. 10

    Boccaletti, S., Latora, V., Moreno, Y., Chavez, M. & Hwang, D.-U. Complex networks: structure and dynamics. Phys. Rep. 424, 175–308 (2006).

  11. 11

    Sporns, O. Cerebral cartography and connectomics. Phil. Trans. R. Soc. B. Biol. Sci. 370, 20140173 (2015).

  12. 12

    Breakspear, M. Dynamic models of large-scale brain activity. Nat. Neurosci. 20, 340–352 (2017). This is a comprehensive review of computational and empirical studies that advance our understanding of collective and nonlinear dynamics in large-scale brain networks.

  13. 13

    Deco, G., Tononi, G., Boly, M. & Kringelbach, M. L. Rethinking segregation and integration: contributions of whole-brain modelling. Nat. Rev. Neurosci. 16, 430–439 (2015).

  14. 14

    Bassett, D. S. & Sporns, O. Network neuroscience. Nat. Neurosci. 20, 353–364 (2017).

  15. 15

    Fornito, A., Zalesky, A. & Bullmore, E. Fundamentals of Brain Network Analysis. (Academic Press, 2016).

  16. 16

    Newman, M. Networks: An Introduction. (OUP Oxford, 2010).

  17. 17

    Estrada, E. The Structure of Complex Networks: Theory and Applications. (OUP Oxford, 2011).

  18. 18

    Barabási, A.-L. Network Science. (Cambridge Univ. Press, 2016).

  19. 19

    Kirst, C., Modes, C. D. & Magnasco, M. O. Shifting attention to dynamics: self-reconfiguration of neural networks. Curr. Opin. Systems Biol. 3, 132–140 (2017).

  20. 20

    Sporns, O. Network attributes for segregation and integration in the human brain. Curr. Opin. Neurobiol. 23, 162–171 (2013).

  21. 21

    Avena-Koenigsberger, A. et al. Path ensembles and a tradeoff between communication efficiency and resilience in the human connectome. Brain Struct. Funct. 222, 603–618 (2017).

  22. 22

    Kaiser, M., Martin, R., Andras, P. & Young, M. P. Simulation of robustness against lesions of cortical networks. Eur. J. Neurosci. 25, 3185–3192 (2007).

  23. 23

    Womelsdorf, T. et al. Modulation of neuronal interactions through neuronal synchronization. Science 316, 1609–1612 (2007).

  24. 24

    Smarandache-Wellmann, C. & Grätsch, S. Mechanisms of coordination in distributed neural circuits: encoding coordinating information. J. Neurosci. 34, 5627–5639 (2014).

  25. 25

    Bassett, D. S. et al. Dynamic reconfiguration of human brain networks during learning. Proc. Natl Acad. Sci. USA 108, 7641–7646 (2011).

  26. 26

    van den Heuvel, M. P. & Sporns, O. An anatomical substrate for integration among functional networks in human cortex. J. Neurosci. 33, 14489–14500 (2013).

  27. 27

    Zamora-López, G., Zhou, C. & Kurths, J. Cortical hubs form a module for multisensory integration on top of the hierarchy of cortical networks. Front. Neuroinform. 4, 1 (2010).

  28. 28

    Gallos, L. K., Makse, H. A. & Sigman, M. A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. Proc. Natl Acad. Sci. USA 109, 2825–2830 (2012).

  29. 29

    Bertolero, M. A., Yeo, B. T. T. & D'Esposito, M. The modular and integrative functional architecture of the human brain. Proc. Natl Acad. Sci. USA 112, E6798–E6807 (2015).

  30. 30

    van den Heuvel, M. P., Bullmore, E. T. & Sporns, O. Comparative connectomics. Trends Cogn. Sci. 20, 345–361 (2016).

  31. 31

    Betzel, R. F. & Bassett, D. S. Multi-scale brain networks. Neuroimage 160, 73–83 (2016).

  32. 32

    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). This review highlights the application of graph theory to studying the trade-offs between biological cost and functional value in small-scale neural networks.

  33. 33

    Passingham, R. E., Stephan, K. E. & Kötter, R. The anatomical basis of functional localization in the cortex. Nat. Rev. Neurosci. 3, 606–616 (2002).

  34. 34

    Kötter, R. & Stephan, K. E. Network participation indices: characterizing component roles for information processing in neural networks. Neural Netw. 16, 1261–1275 (2003).

  35. 35

    Watts, D. J. & Strogatz, S. H. Collective dynamics of 'small-world' networks. Nature 393, 440–442 (1998).

  36. 36

    Bullmore, E. & Sporns, O. The economy of brain network organization. Nat. Rev. Neurosci. 13, 336–349 (2012).

  37. 37

    Betzel, R. F. et al. Generative models of the human connectome. Neuroimage 124, 1054–1064 (2016).

  38. 38

    Raj, A. & Chen, Y.-H. The wiring economy principle: connectivity determines anatomy in the human brain. PLoS ONE 6, e14832 (2011).

  39. 39

    Kaiser, M. & Hilgetag, C. C. Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Comput. Biol. 2, e95 (2006).

  40. 40

    Rubinov, M., Ypma, R. J. F., Watson, C. & Bullmore, E. T. Wiring cost and topological participation of the mouse brain connectome. Proc. Natl Acad. Sci. USA 112, 10032–10037 (2015).

  41. 41

    Goni, J. et al. Resting-brain functional connectivity predicted by analytic measures of network communication. Proc. Natl Acad. Sci. USA 111, 833–838 (2013).

  42. 42

    Bettinardi, R. G. et al. How structure sculpts function: unveiling the contribution of anatomical connectivity to the brain's spontaneous correlation structure. Chaos 27, 047409 (2017). This paper introduces a measure that quantifies the propensity of two nodes to dynamically correlate, given the structural connectivity patterns that constrain the spread of information.

  43. 43

    Achard, S., Salvador, R., Whitcher, B., Suckling, J. & Bullmore, E. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J. Neurosci. 26, 63–72 (2006).

  44. 44

    Hermundstad, A. M. et al. Structural foundations of resting-state and task-based functional connectivity in the human brain. Proc. Natl Acad. Sci. USA 110, 6169–6174 (2013).

  45. 45

    van den Heuvel, M. P., Stam, C. J., Kahn, R. S. & Hulshoff Pol, H. E. Efficiency of functional brain networks and intellectual performance. J. Neurosci. 29, 7619–7624 (2009).

  46. 46

    Bassett, D. S. & Bullmore, E. Small-world brain networks. Neuroscientist 12, 512–523 (2006).

  47. 47

    de Pasquale, F., Della Penna, S., Sporns, O., Romani, G. L. & Corbetta, M. A. Dynamic core network and global efficiency in the resting human brain. Cereb. Cortex 26, 4015–4033 (2016).

  48. 48

    Hearne, L. J., Cocchi, L., Zalesky, A. & Mattingley, J. B. Reconfiguration of brain network architectures between resting state and complexity-dependent cognitive reasoning. J. Neurosci. 37, 8399–8411 (2017).

  49. 49

    Kabbara, A., El Falou, W., Khalil, M., Wendling, F. & Hassan, M. The dynamic functional core network of the human brain at rest. Sci. Rep. 7, 2936 (2017).

  50. 50

    Boguñá, M., Krioukov, D. & Claffy, K. C. Navigability of complex networks. Nat. Phys. 5, 74–80 (2008).

  51. 51

    Goñi, J. et al. Exploring the morphospace of communication efficiency in complex networks. PLoS ONE 8, e58070 (2013). This article introduces the concept of diffusion efficiency, and maps the topological characteristics of networks that optimize diffusion and routing efficiency onto a morphospace.

  52. 52

    Abdelnour, F., Voss, H. U. & Raj, A. Network diffusion accurately models the relationship between structural and functional brain connectivity networks. Neuroimage 90, 335–347 (2014).

  53. 53

    Mišić, B., Sporns, O. & McIntosh, A. R. Communication efficiency and congestion of signal traffic in large-scale brain networks. PLoS Comput. Biol. 10, e1003427 (2014).

  54. 54

    Graham, D. & Rockmore, D. The packet switching brain. J. Cogn. Neurosci. 23, 267–276 (2011).

  55. 55

    Graham, D. J. Routing in the brain. Front. Comput. Neurosci. 8, 44 (2014).

  56. 56

    Rodrigues, F. A. & da Fontoura Costa, L. A structure–dynamic approach to cortical organization: number of paths and accessibility. J. Neurosci. Methods 183, 57–62 (2009).

  57. 57

    Wook Yoo, S. et al. A network flow-based analysis of cognitive reserve in normal ageing and Alzheimer's disease. Sci. Rep. 5, 10057 (2015).

  58. 58

    Di Lanzo, C., Marzetti, L., Zappasodi, F., De Vico Fallani, F. & Pizzella, V. Redundancy as a graph-based index of frequency specific MEG functional connectivity. Comput. Math. Methods Med. 2012, 1–9 (2012).

  59. 59

    De Vico Fallani, F. et al. Multiple pathways analysis of brain functional networks from EEG signals: an application to real data. Brain Topogr. 23, 344–354 (2011).

  60. 60

    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).

  61. 61

    Calhoun, V. D., Miller, R., Pearlson, G. & Adalı, T. The chronnectome: time-varying connectivity networks as the next frontier in fMRI data discovery. Neuron 84, 262–274 (2014).

  62. 62

    Gonzalez-Castillo, J. et al. Tracking ongoing cognition in individuals using brief, whole-brain functional connectivity patterns. Proc. Natl Acad. Sci. USA 112, 8762–8767 (2015).

  63. 63

    Siegel, M., Buschman, T. J. & Miller, E. K. Cortical information flow during flexible sensorimotor decisions. Science 348, 1352–1355 (2015). This paper exemplifies how empirical studies can trace complex patterns of information flow in brain networks, for example between the frontal cortex and posterior cortex.

  64. 64

    Siegel, M., Donner, T. H. & Engel, A. K. Spectral fingerprints of large-scale neuronal interactions. Nat. Rev. Neurosci. 13, 121–134 (2012).

  65. 65

    Lawrence, S. J. D., Formisano, E., Muckli, L. & de Lange, F. P. Laminar fMRI: applications for cognitive neuroscience. Neuroimage (2017).

  66. 66

    Honey, C. J. et al. Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl Acad. Sci. USA 106, 2035–2040 (2009).

  67. 67

    Rubinov, M. & Sporns, O. Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059–1069 (2010).

  68. 68

    Zalesky, A., Fornito, A. & Bullmore, E. On the use of correlation as a measure of network connectivity. Neuroimage 60, 2096–2106 (2012).

  69. 69

    Adachi, Y. et al. Functional connectivity between anatomically unconnected areas is shaped by collective network-level effects in the macaque cortex. Cereb. Cortex 22, 1586–1592 (2012).

  70. 70

    Mitra, A. & Raichle, M. E. How networks communicate: propagation patterns in spontaneous brain activity. Phil. Trans. R. Soc. B 371, 20150546 (2016).

  71. 71

    Ding, M., Chen, Y. & Bressler, S. L. in Handbook of Time Series Analysis (eds Schelter, B., Winterhalder, M. & Timmer, J.) 437–460 (Wiley, 2006).

  72. 72

    Vicente, R., Wibral, M., Lindner, M. & Pipa, G. Transfer entropy — a model-free measure of effective connectivity for the neurosciences. J. Comput. Neurosci. 30, 45–67 (2010).

  73. 73

    Lobier, M., Siebenhühner, F., Palva, S. & Palva, J. M. Phase transfer entropy: a novel phase-based measure for directed connectivity in networks coupled by oscillatory interactions. Neuroimage 85, 853–872 (2014).

  74. 74

    Bastos, A. M. & Schoffelen, J.-M. A. A tutorial review of functional connectivity analysis methods and their interpretational pitfalls. Front. Syst. Neurosci. 9, 175 (2015).

  75. 75

    Akam, T. & Kullmann, D. M. Oscillatory multiplexing of population codes for selective communication in the mammalian brain. Nat. Rev. Neurosci. 15, 111–122 (2014).

  76. 76

    Helfrich, R. F. & Knight, R. T. Oscillatory dynamics of prefrontal cognitive control. Trends Cogn. Sci. 20, 916–930 (2016).

  77. 77

    Hillebrand, A. et al. Direction of information flow in large-scale resting-state networks is frequency-dependent. Proc. Natl Acad. Sci. USA 113, 3867–3872 (2016).

  78. 78

    Griffa, A. et al. Transient networks of spatio-temporal connectivity map communication pathways in brain functional systems. Neuroimage 155, 490–502 (2017). This novel multilayer-network model captures the propagation of functional activity through the underlying anatomical structure.

  79. 79

    Latora, V. & Marchiori, M. Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 (2001).

  80. 80

    Borgatti, S. P. Centrality and network flow. Soc. Networks 27, 55–71 (2005).

  81. 81

    Pavlovic, D. M., Vértes, P. E., Bullmore, E. T., Schafer, W. R. & Nichols, T. E. Stochastic blockmodeling of the modules and core of the Caenorhabditis elegans connectome. PLoS ONE 9, e97584 (2014).

  82. 82

    Dumoulin, S. O. in Biological Magnetic Resonance (ed. Berliner, L.) 429–471 (Springer, 2015).

  83. 83

    Wertz, A. et al. Single-cell-initiated monosynaptic tracing reveals layer-specific cortical network modules. Science 349, 70–74 (2015).

  84. 84

    Lee, W.-C. A. et al. Anatomy and function of an excitatory network in the visual cortex. Nature 532, 370–374 (2016).

  85. 85

    Kennedy, H., Van Essen, D. C. & Christen, Y. (eds) Micro-, Meso- and Macro-Connectomics of the Brain. (Springer, 2017).

  86. 86

    Sporns, O. & Betzel, R. F. Modular brain networks. Annu. Rev. Psychol. 67, 613–640 (2016).

  87. 87

    Baum, G. L. et al. Modular segregation of structural brain networks supports the development of executive function in youth. Curr. Biol. 27, 1561–1572 (2017).

  88. 88

    Nematzadeh, A., Ferrara, E., Flammini, A. & Ahn, Y.-Y. Optimal network modularity for information diffusion. Phys. Rev. Lett. 113, 088701 (2014).

  89. 89

    Meunier, D., Lambiotte, R. & Bullmore, E. T. Modular and hierarchically modular organization of brain networks. Front. Neurosci. 4, 200 (2010).

  90. 90

    Zamora-López, G., Zhou, C. & Kurths, J. Graph analysis of cortical networks reveals complex anatomical communication substrate. Chaos 19, 015117 (2009).

  91. 91

    Brovelli, A. et al. Dynamic reconfiguration of visuomotor-related functional connectivity networks. J. Neurosci. 37, 839–853 (2017).

  92. 92

    Wang, L., Saalmann, Y. B., Pinsk, M. A., Arcaro, M. J. & Kastner, S. Electrophysiological low-frequency coherence and cross-frequency coupling contribute to BOLD connectivity. Neuron 76, 1010–1020 (2012).

  93. 93

    Betzel, R. F. et al. The modular organization of human anatomical brain networks: accounting for the cost of wiring. Network Neurosci. 1, 42–68 (2017).

  94. 94

    Mišić, B. et al. Network-level structure–function relationships in human neocortex. Cereb. Cortex 26, 3285–3296 (2016).

  95. 95

    Sneppen, K., Trusina, A. & Rosvall, M. Hide-and-seek on complex networks. Europhys. Lett. 69, 853–859 (2005).

  96. 96

    Rosvall, M., Grönlund, A., Minnhagen, P. & Sneppen, K. Searchability of networks. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72, 046117 (2005).

  97. 97

    Fornito, A. & Bullmore, E. T. Reconciling abnormalities of brain network structure and function in schizophrenia. Curr. Opin. Neurobiol. 30, 44–50 (2015).

  98. 98

    van den Heuvel, M. P. & Sporns, O. Rich-club organization of the human connectome. J. Neurosci. 31, 15775–15786 (2011).

  99. 99

    Cole, M. W., Ito, T., Bassett, D. S. & Schultz, D. H. Activity flow over resting-state networks shapes cognitive task activations. Nat. Neurosci. 19, 1718–1726 (2016).

  100. 100

    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).

  101. 101

    van den Heuvel, M. P., Kahn, R. S., Goni, J. & Sporns, O. High-cost, high-capacity backbone for global brain communication. Proc. Natl Acad. Sci. USA 109, 11372–11377 (2012).

  102. 102

    Suckling, J. et al. A winding road: Alzheimer's disease increases circuitous functional connectivity pathways. Front. Comput. Neurosci. 9, 140 (2015).

  103. 103

    Kaiser, M. Mechanisms of connectome development. Trends Cogn. Sci. 21, 703–717 (2017).

  104. 104

    Estrada, E. & Hatano, N. Communicability in complex networks. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77, 036111 (2008).

  105. 105

    Crofts, J. J. et al. Network analysis detects changes in the contralesional hemisphere following stroke. Neuroimage 54, 161–169 (2011).

  106. 106

    Grayson, D. S. et al. The rhesus monkey connectome predicts disrupted functional networks resulting from pharmacogenetic inactivation of the amygdala. Neuron 91, 453–466 (2016).

  107. 107

    Zylberberg, A., Slezak, D. F., Roelfsema, P. R., Dehaene, S. & Sigman, M. The brain's router: a cortical network model of serial processing in the primate brain. PLoS Comput. Biol. 6, e1000765 (2010).

  108. 108

    Laughlin, S. B. Energy as a constraint on the coding and processing of sensory information. Curr. Opin. Neurobiol. 11, 475–480 (2001).

  109. 109

    Yin, C.-Y., Wang, B.-H., Wang, W.-X., Zhou, T. & Yang, H.-J. Efficient routing on scale-free networks based on local information. Phys. Lett. A 351, 220–224 (2006).

  110. 110

    Yang, S.-J. Exploring complex networks by walking on them. Phys. Rev. E 71, 016107 (2005).

  111. 111

    Rosvall, M. & Bergstrom, C. T. Maps of random walks on complex networks reveal community structure. Proc. Natl Acad. Sci. USA 105, 1118–1123 (2008).

  112. 112

    Timme, N. M. et al. High-degree neurons feed cortical computations. PLoS Comput. Biol. 12, e1004858 (2016).

  113. 113

    Snell, J. L., Laurie Snell, J. & Ito, K. Introduction to probability theory. J. Am. Stat. Assoc. 81, 857 (1986).

  114. 114

    Avena-Koenigsberger, A. et al. Using Pareto optimality to explore the topology and dynamics of the human connectome. Phil. Trans. R. Soc. B 369, 20130530 (2014).

  115. 115

    Delvenne, J. C., Yaliraki, S. N. & Barahona, M. Stability of graph communities across time scales. Proc. Natl Acad. Sci. USA 107, 12755–12760 (2010).

  116. 116

    Betzel, R. F. et al. Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity. Network Sci. 1, 353–373 (2013).

  117. 117

    van den Heuvel, M. P. & Sporns, O. Network hubs in the human brain. Trends Cogn. Sci. 17, 683–696 (2013).

  118. 118

    Spreng, R. N. et al. Intrinsic architecture underlying the relations among the default, dorsal attention, and frontoparietal control networks of the human brain. J. Cogn. Neurosci. 25, 74–86 (2013).

  119. 119

    Sepulcre, J., Sabuncu, M. R., Yeo, T. B., Liu, H. & Johnson, K. A. Stepwise connectivity of the modal cortex reveals the multimodal organization of the human brain. J. Neurosci. 32, 10649–10661 (2012).

  120. 120

    Braga, R. M., Sharp, D. J., Leeson, C., Wise, R. J. S. & Leech, R. Echoes of the brain within default mode, association, and heteromodal cortices. J. Neurosci. 33, 14031–14039 (2013).

  121. 121

    Bacik, K. A., Schaub, M. T., Beguerisse-Díaz, M., Billeh, Y. N. & Barahona, M. Flow-based network analysis of the Caenorhabditis elegans connectome. PLoS Comput. Biol. 12, e1005055 (2016).

  122. 122

    Galán, R. F. On how network architecture determines the dominant patterns of spontaneous neural activity. PLoS ONE e2148 (2008).

  123. 123

    Mišić, B., Goñi, J., Betzel, R. F., Sporns, O. & McIntosh, A. R. A network convergence zone in the hippocampus. PLoS Comput. Biol. 10, e1003982 (2014).

  124. 124

    Kaiser, M. & Hilgetag, C. C. Edge vulnerability in neural and metabolic networks. Biol. Cybern. 90, 311–317 (2004).

  125. 125

    O'Dea, R., Crofts, J. J. & Kaiser, M. Spreading dynamics on spatially constrained complex brain networks. J. R. Soc. Interface 10, 20130016 (2013).

  126. 126

    Mišić, B. et al. Cooperative and competitive spreading dynamics on the human connectome. Neuron 86, 1518–1529 (2015). This study applies a spreading model to investigate spreading dynamics in human brain networks. Cascades emerging from the spreading dynamics converge on polysensory associative areas, highlighting the integrative capacity of the topology of the network.

  127. 127

    Worrell, J. C., Rumschlag, J., Betzel, R. F., Sporns, O. & Mišić, B. Optimized connectome architecture for sensory-motor integration. Network Neurosci. (2017).

  128. 128

    Raj, A., Kuceyeski, A. & Weiner, M. A network diffusion model of disease progression in dementia. Neuron 73, 1204–1215 (2012).

  129. 129

    Stam, C. J. et al. The relation between structural and functional connectivity patterns in complex brain networks. Int. J. Psychophysiol. 103, 149–160 (2016).

  130. 130

    Gollo, L. L., Copelli, M. & Roberts, J. A. Diversity improves performance in excitable networks. PeerJ 4, e1912 (2016).

  131. 131

    Beggs, J. M. & Plenz, D. Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177 (2003).

  132. 132

    Deco, G., Jirsa, V. K., Robinson, P. A., Breakspear, M. & Friston, K. The dynamic brain: from spiking neurons to neural masses and cortical fields. PLoS Comput. Biol. 4, e1000092 (2008).

  133. 133

    Ghosh, A., Rho, Y., McIntosh, A. R., Kötter, R. & Jirsa, V. K. Cortical network dynamics with time delays reveals functional connectivity in the resting brain. Cogn. Neurodyn. 2, 115–120 (2008).

  134. 134

    Deco, G., Jirsa, V., McIntosh, A. R., Sporns, O. & Kötter, R. Key role of coupling, delay, and noise in resting brain fluctuations. Proc. Natl Acad. Sci. USA 106, 10302–10307 (2009).

  135. 135

    Freyer, F. et al. Biophysical mechanisms of multistability in resting-state cortical rhythms. J. Neurosci. 31, 6353–6361 (2011).

  136. 136

    Deco, G. & Kringelbach, M. Metastability and coherence: extending the communication through coherence hypothesis using a whole-brain computational perspective. Trends Neurosci. 39, 432 (2016).

  137. 137

    Ni, J. et al. Gamma-rhythmic gain modulation. Neuron 92, 240–251 (2016).

  138. 138

    Vazquez-Rodriguez, B. et al. Stochastic resonance at criticality in a network model of the human cortex. Sci. Rep. 7, 13020 (2017).

  139. 139

    Ghosh, A., Rho, Y., McIntosh, A. R., Kötter, R. & Jirsa, V. K. Noise during rest enables the exploration of the brain's dynamic repertoire. PLoS Comput. Biol. 4, e1000196 (2008).

  140. 140

    Faisal, A. A., Aldo Faisal, A., Selen, L. P. J. & Wolpert, D. M. Noise in the nervous system. Nat. Rev. Neurosci. 9, 292–303 (2008).

  141. 141

    Palmigiano, A., Geisel, T., Wolf, F. & Battaglia, D. Flexible information routing by transient synchrony. Nat. Neurosci. 20, 1014–1022 (2017).

  142. 142

    Bijsterbosch, J., Smith, S. M. & Beckmann, C. F. (eds) An Introduction to Resting State FMRI Functional Connectivity. (Oxford Univ. Press, 2017).

  143. 143

    Englot, D. J. et al. Functional connectivity disturbances of the ascending reticular activating system in temporal lobe epilepsy. J. Neurol. Neurosurg. Psychiatry 88, 925–932 (2017).

  144. 144

    Lee, D. et al. Analysis of structure-function network decoupling in the brain systems of spastic diplegic cerebral palsy. Hum. Brain Mapp. 38, 5292–5306 (2017).

  145. 145

    Yaesoubi, M., Allen, E. A., Miller, R. L. & Calhoun, V. D. Dynamic coherence analysis of resting fMRI data to jointly capture state-based phase, frequency, and time-domain information. Neuroimage 120, 133–142 (2015).

  146. 146

    Seth, A. K., Barrett, A. B. & Barnett, L. Granger causality analysis in neuroscience and neuroimaging. J. Neurosci. 35, 3293–3297 (2015).

  147. 147

    Mill, R. D., Bagic, A., Bostan, A., Schneider, W. & Cole, M. W. Empirical validation of directed functional connectivity. Neuroimage 146, 275–287 (2017).

  148. 148

    Friston, K. J., Harrison, L. & Penny, W. Dynamic causal modelling. Neuroimage 19, 1273–1302 (2003).

  149. 149

    Razi, A. et al. Large-scale DCMs for resting state fMRI. Network Neurosci. 1, 222–241 (2017).

  150. 150

    Seghier, M. L. & Friston, K. J. Network discovery with large DCMs. Neuroimage 68, 181–191 (2013).

  151. 151

    Khambhati, A. N., Sizemore, A. E., Betzel, R. F. & Bassett, D. S. Modeling and interpreting mesoscale network dynamics. Neuroimage (2017).

  152. 152

    Hutchison, R. M. et al. Dynamic functional connectivity: promise, issues, and interpretations. Neuroimage 80, 360–378 (2013).

  153. 153

    Gonzalez-Castillo, J. & Bandettini, P. A. Task-based dynamic functional connectivity: recent findings and open questions. Neuroimage (2017).

  154. 154

    Bassett, D. S., Yang, M., Wymbs, N. F. & Grafton, S. T. Learning-induced autonomy of sensorimotor systems. Nat. Neurosci. 18, 744–751 (2015).

  155. 155

    Cole, M. W. et al. Multi-task connectivity reveals flexible hubs for adaptive task control. Nat. Neurosci. 16, 1348–1355 (2013).

  156. 156

    Krienen, F. M., Yeo, B. T. T. & Buckner, R. L. Reconfigurable task-dependent functional coupling modes cluster around a core functional architecture. Phil. Trans. R. Soc. B. Biol. Sci. 369, 20130526 (2014).

  157. 157

    Bassett, D. S. et al. Task-based core-periphery organization of human brain dynamics. PLoS Comput. Biol. 9, e1003171 (2013).

  158. 158

    Cole, M. W., Bassett, D. S., Power, J. D., Braver, T. S. & Petersen, S. E. Intrinsic and task-evoked network architectures of the human brain. Neuron 83, 238–251 (2014).

  159. 159

    Braun, U. et al. Dynamic reconfiguration of frontal brain networks during executive cognition in humans. Proc. Natl Acad. Sci. USA 112, 11678–11683 (2015).

  160. 160

    Varela, F., Lachaux, J. P., Rodriguez, E. & Martinerie, J. The brainweb: phase synchronization and large-scale integration. Nat. Rev. Neurosci. 2, 229–239 (2001).

  161. 161

    Fries, P. A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends Cogn. Sci. 9, 474–480 (2005).

  162. 162

    Kirst, C., Timme, M. & Battaglia, D. Dynamic information routing in complex networks. Nat. Commun. 7, 11061 (2016). This study presents a mechanism that generates flexible information-routing patterns on top of the collective dynamics of the network.

  163. 163

    Gollo, L. L., Roberts, J. A. & Cocchi, L. Mapping how local perturbations influence systems-level brain dynamics. Neuroimage 160, 97–112 (2017). This study of local perturbation effects on human brain networks highlights the importance of the core–periphery structure of the underlying anatomy.

  164. 164

    Dayan, E., Censor, N., Buch, E. R., Sandrini, M. & Cohen, L. G. Noninvasive brain stimulation: from physiology to network dynamics and back. Nat. Neurosci. 16, 838–844 (2013).

  165. 165

    Matsumoto, R. et al. Functional connectivity in the human language system: a cortico-cortical evoked potential study. Brain 127, 2316–2330 (2004).

  166. 166

    Friston, K. The free-energy principle: a rough guide to the brain? Trends Cogn. Sci. 13, 293–301 (2009).

  167. 167

    Friston, K. J., Parr, T. & de Vries, B. The graphical brain: belief propagation and active inference. Network Neurosci. (2017).

  168. 168

    Voytek, B. & Knight, R. T. Dynamic network communication as a unifying neural basis for cognition, development, aging, and disease. Biol. Psychiatry 77, 1089–1097 (2015).

  169. 169

    Cocchi, L. et al. A hierarchy of timescales explains distinct effects of local inhibition of primary visual cortex and frontal eye fields. eLife 5, e15252 (2016).

  170. 170

    Ramon y Cajal, S. Histology of the Nervous System of Man and Vertebrates. (Oxford Univ. Press, 1995).

  171. 171

    Borst, A. & Theunissen, F. E. Information theory and neural coding. Nat. Neurosci. 2, 947–957 (1999).

  172. 172

    Balasubramanian, V. & Berry, M. A test of metabolically efficient coding in the retina. Network Comput. Neural Systems 13, 531–552 (2002).

  173. 173

    Gulyás, A., Bíró, J. J., Kőrösi, A., Rétvári, G. & Krioukov, D. Navigable networks as Nash equilibria of navigation games. Nat. Commun. 6, 7651 (2015).

  174. 174

    Barthélemy, M. Spatial networks. Phys. Rep. 499, 1–101 (2011).

  175. 175

    Simas, T. & Rocha, L. M. Distance closures on complex networks. Network Sci. 3, 227–268 (2015).

  176. 176

    Leong, A. T. L. et al. Long-range projections coordinate distributed brain-wide neural activity with a specific spatiotemporal profile. Proc. Natl Acad. Sci. USA 113, E8306–E8315 (2016). This study demonstrates that long-range interactions in large-scale brain networks are governed by low-frequency activity.

  177. 177

    Simas, T. et al. Semi-metric topology of the human connectome: sensitivity and specificity to autism and major depressive disorder. PLoS ONE 10, e0136388 (2015).

  178. 178

    Avena-Koenigsberger, A., Goñi, J., Solé, R. & Sporns, O. Network morphospace. J. R. Soc. Interface 12, 20140881 (2015). Combining concepts from evolutionary biology and network science, this article lays out the steps to conduct a network morphospace analysis, highlighting the potential of this framework to uncover the design rules and constraints that drive and shape the topology of a network.

  179. 179

    Solé, R. V., Ferrer-Cancho, R., Montoya, J. M. & Valverde, S. Selection, tinkering, and emergence in complex networks. Complexity 8, 20–33 (2002).

  180. 180

    Clune, J., Mouret, J.-B. & Lipson, H. The evolutionary origins of modularity. Proc. Biol. Sci. 280, 20122863 (2013).

  181. 181

    Churchland, P. S. & Sejnowski, T. J. The Computational Brain. (MIT Press,1994).

  182. 182

    Fodor, J. A. & Pylyshyn, Z. W. Connectionism and cognitive architecture: a critical analysis. Cognition 28, 3–71 (1988).

  183. 183

    Marr, D., Ullman, S. & Poggio, T. A. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. (MIT Press, 2010).

  184. 184

    Matthei, E. H. & Fodor, J. A. The modularity of mind: an essay on faculty psychology. Language 60, 976 (1984).

  185. 185

    Bassett, D. S. & Mattar, M. G. A. Network neuroscience of human learning: potential to inform quantitative theories of brain and behavior. Trends Cogn. Sci. 21, 250–264 (2017).

  186. 186

    Shenhav, A. et al. Toward a rational and mechanistic account of mental effort. Annu. Rev. Neurosci. 40, 99–124 (2017).

  187. 187

    Schroeter, M. S., Charlesworth, P., Kitzbichler, M. G., Paulsen, O. & Bullmore, E. T. Emergence of rich-club topology and coordinated dynamics in development of hippocampal functional networks in vitro. J. Neurosci. 35, 5459–5470 (2015).

  188. 188

    Nigam, S. et al. Rich-club organization in effective connectivity among cortical neurons. J. Neurosci. 36, 670–684 (2016). This is a study of the network topology of directed functional interactions between neurons recorded at high temporal resolution.

Download references


The authors gratefully acknowledge insightful discussions with R. F. Betzel and J. Goñi. O.S. acknowledges support from the Indiana Clinical Translational Sciences Institute (NIH UL1TR0011808), the James S. McDonnell Foundation (220020387), the National Science Foundation (1636892) and the US National Institutes of Health (R01-AT009036, R01-B022574 and P30-AG010133). B.M. acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant RGPIN #017-04265) and from the Fonds de recherche du Quebec - Santé.

Author information

The authors all researched data for the article, provided a substantial contribution to discussion of the content, wrote the article and reviewed and edited the manuscript before submission.

Correspondence to Olaf Sporns.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

PowerPoint slides


Random walk

A stochastic process that describes a succession of random steps taken on a network.

Network topology

The patterns of connectivity of a network.

Neural elements

Unit elements of a neural network. The unit is defined by the spatial scale. Neural elements can represent, for example, a single synapse, a neuron, a neuronal population or an entire brain region.

Adjacency matrix

A mathematical representation of a network as a matrix. Elements of the matrix indicate whether two nodes are connected or not.


A network's ability to adapt and/or recover from structural failures.

Betweenness centrality

A nodal measure of influence determined by the proportion of shortest paths that traverse a node.


The process of sending a message or signal through a determined path.

Fibre tracts

A bundle of axons connecting two brain regions.

Search information

The amount of information needed to discover a path in a network.

Edge weight

A measure of the strength of the relationship between two connected nodes.

Connection density

The fraction of connections present in a network, or a subsystem of a network, with respect to the maximum number of possible connections.


A space in which possible, impossible and real-world network architectures can be mapped.


Highly connected nodes.

Path transitivity

The frequency of detours comprising two edges (that is, of length 2) that are available along a path.


A tendency for a network to contain a densely interconnected central component.


Propensity for nodes to form internally densely connected clusters.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Avena-Koenigsberger, A., Misic, B. & Sporns, O. Communication dynamics in complex brain networks. Nat Rev Neurosci 19, 17–33 (2018) doi:10.1038/nrn.2017.149

Download citation

Further reading