The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics and has been widely undertaken. Typically, however, networks employed in theoretical studies bear little relation to the spatial embedding or connectivity of the neural networks that they attempt to replicate. Here, we employ detailed neuroimaging data to define a network whose spatial embedding represents accurately the folded structure of the cortical surface of a rat brain and investigate the propagation of activity over this network under simple spreading and connectivity rules. By comparison with standard network models with the same coarse statistics, we show that the cortical geometry influences profoundly the speed of propagation of activation through the network. Our conclusions are of high relevance to the theoretical modelling of epileptic seizure events and indicate that such studies which omit physiological network structure risk simplifying the dynamics in a potentially significant way.
spreading dynamics; network science; neuroscience; epilepsy; connectome
Neuronal signal integration and information processing in cortical networks critically depend on the organization of synaptic connectivity. During development, neurons can form synaptic connections when their axonal and dendritic arborizations come within close proximity of each other. Although many signaling cues are thought to be involved in guiding neuronal extensions, the extent to which accidental appositions between axons and dendrites can already account for synaptic connectivity remains unclear. To investigate this, we generated a local network of cortical L2/3 neurons that grew out independently of each other and that were not guided by any extracellular cues. Synapses were formed when axonal and dendritic branches came by chance within a threshold distance of each other. Despite the absence of guidance cues, we found that the emerging synaptic connectivity showed a good agreement with available experimental data on spatial locations of synapses on dendrites and axons, number of synapses by which neurons are connected, connection probability between neurons, distance between connected neurons, and pattern of synaptic connectivity. The connectivity pattern had a small-world topology but was not scale free. Together, our results suggest that baseline synaptic connectivity in local cortical circuits may largely result from accidentally overlapping axonal and dendritic branches of independently outgrowing neurons.
Evidence from anatomical and functional imaging studies have highlighted major modifications of cortical circuits during adolescence. These include reductions of gray matter (GM), increases in the myelination of cortico-cortical connections and changes in the architecture of large-scale cortical networks. It is currently unclear, however, how the ongoing developmental processes impact upon the folding of the cerebral cortex and how changes in gyrification relate to maturation of GM/WM-volume, thickness and surface area. In the current study, we acquired high-resolution (3 Tesla) magnetic resonance imaging (MRI) data from 79 healthy subjects (34 males and 45 females) between the ages of 12 and 23 years and performed whole brain analysis of cortical folding patterns with the gyrification index (GI). In addition to GI-values, we obtained estimates of cortical thickness, surface area, GM and white matter (WM) volume which permitted correlations with changes in gyrification. Our data show pronounced and widespread reductions in GI-values during adolescence in several cortical regions which include precentral, temporal and frontal areas. Decreases in gyrification overlap only partially with changes in the thickness, volume and surface of GM and were characterized overall by a linear developmental trajectory. Our data suggest that the observed reductions in GI-values represent an additional, important modification of the cerebral cortex during late brain maturation which may be related to cognitive development.
Graph theoretical approaches have successfully revealed abnormality in brain connectivity, in particular, for contrasting patients from healthy controls. Besides the group comparison analysis, a correlational study is also challenging. In studies with patients, for example, finding brain connections that indeed deepen specific symptoms is interesting. The correlational study is also beneficial since it does not require controls, which are often difficult to find, especially for old-age patients with cognitive impairment where controls could also have cognitive deficits due to normal ageing. However, one of the major difficulties in such correlational studies is too conservative multiple comparison correction. In this paper, we propose a novel method for identifying brain connections that are correlated with a specific cognitive behavior by employing cluster-based statistics, which is less conservative than other methods, such as Bonferroni correction, false discovery rate procedure, and extreme statistics. Our method is based on the insight that multiple brain connections, rather than a single connection, are responsible for abnormal behaviors. Given brain connectivity data, we first compute a partial correlation coefficient between every edge and the behavioral measure. Then we group together neighboring connections with strong correlation into clusters and calculate their maximum sizes. This procedure is repeated for randomly permuted assignments of behavioral measures. Significance levels of the identified sub-networks are estimated from the null distribution of the cluster sizes. This method is independent of network construction methods: either structural or functional network can be used in association with any behavioral measures. We further demonstrated the efficacy of our method using patients with subcortical vascular cognitive impairment. We identified sub-networks that are correlated with the disease severity by exploiting diffusion tensor imaging techniques. The identified sub-networks were consistent with the previous clinical findings having valid significance level, while other methods did not assert any significant findings.
Psychogenic non-epileptic seizures (PNES) are paroxysmal behaviors that resemble epileptic seizures but lack abnormal electrical activity. Recent studies suggest aberrant functional connectivity involving specific brain regions in PNES. Little is known, however, about alterations of topological organization of whole-brain functional and structural connectivity networks in PNES. We constructed functional connectivity networks from resting-state functional MRI signal correlations and structural connectivity networks from diffusion tensor imaging tractography in 17 PNES patients and 20 healthy controls. Graph theoretical analysis was employed to compute network properties. Moreover, we investigated the relationship between functional and structural connectivity networks. We found that PNES patients exhibited altered small-worldness in both functional and structural networks and shifted towards a more regular (lattice-like) organization, which could serve as a potential imaging biomarker for PNES. In addition, many regional characteristics were altered in structural connectivity network, involving attention, sensorimotor, subcortical and default-mode networks. These regions with altered nodal characteristics likely reflect disease-specific pathophysiology in PNES. Importantly, the coupling strength of functional-structural connectivity was decreased and exhibited high sensitivity and specificity to differentiate PNES patients from healthy controls, suggesting that the decoupling strength of functional-structural connectivity might be an important characteristic reflecting the mechanisms of PNES. This is the first study to explore the altered topological organization in PNES combining functional and structural connectivity networks, providing a new way to understand the pathophysiological mechanisms of PNES.
Functional magnetic resonance imaging recordings in the resting-state (RS) from the human brain are characterized by spontaneous low-frequency fluctuations in the blood oxygenation level dependent signal that reveal functional connectivity (FC) via their spatial synchronicity. This RS study applied network analysis to compare FC between late-life depression (LLD) patients and control subjects. Raw cross-correlation matrices (CM) for LLD were characterized by higher FC. We analyzed the small-world (SW) and modular organization of these networks consisting of 110 nodes each as well as the connectivity patterns of individual nodes of the basal ganglia. Topological network measures showed no significant differences between groups. The composition of top hubs was similar between LLD and control subjects, however in the LLD group posterior medial-parietal regions were more highly connected compared to controls. In LLD, a number of brain regions showed connections with more distant neighbors leading to an increase of the average Euclidean distance between connected regions compared to controls. In addition, right caudate nucleus connectivity was more diffuse in LLD. In summary, LLD was associated with overall increased FC strength and changes in the average distance between connected nodes, but did not lead to global changes in SW or modular organization.
late-life depression; aging; resting-state; functional connectivity; default mode network; network analysis; graph theory; functional magnetic resonance
The human connectome at the level of fiber tracts between brain regions has been shown to differ in patients with brain disorders compared to healthy control groups. Nonetheless, there is a potentially large number of different network organizations for individual patients that could lead to cognitive deficits prohibiting correct diagnosis. Therefore changes that can distinguish groups might not be sufficient to diagnose the disease that an individual patient suffers from and to indicate the best treatment option for that patient. We describe the challenges introduced by the large variability of connectomes within healthy subjects and patients and outline three common strategies to use connectomes as biomarkers of brain diseases. Finally, we propose a fourth option in using models of simulated brain activity (the dynamic connectome) based on structural connectivity rather than the structure (connectome) itself as a biomarker of disease. Dynamic connectomes, in addition to currently used structural, functional, or effective connectivity, could be an important future biomarker for clinical applications.
brain connectivity; network disease; brain disorders; classification; diagnosis
Short Term Plasticity (STP) has been shown to exist extensively in synapses throughout the brain. Its function is more or less clear in the sense that it alters the probability of synaptic transmission at short time scales. However, it is still unclear what effect STP has on the dynamics of neural networks. We show, using a novel dynamic STP model, that Short Term Depression (STD) can affect the phase of frequency coded input such that small networks can perform temporal signal summation and determination with high accuracy. We show that this property of STD can readily solve the problem of the ghost frequency, the perceived pitch of a harmonic complex in absence of the base frequency. Additionally, we demonstrate that this property can explain dynamics in larger networks. By means of two models, one of chopper neurons in the Ventral Cochlear Nucleus and one of a cortical microcircuit with inhibitory Martinotti neurons, it is shown that the dynamics in these microcircuits can reliably be reproduced using STP. Our model of STP gives important insights into the potential roles of STP in self-regulation of cortical activity and long-range afferent input in neuronal microcircuits.
Graph-theoretical analysis of brain connectivity data has revealed significant features of brain network organization across a range of species. Consistently, large-scale anatomical networks exhibit highly nonrandom attributes including an efficient small world modular architecture, with distinct network communities that are interlinked by hub regions. The functional importance of hubs motivates a closer examination of their mutual interconnections, specifically to examine the hypothesis that hub regions are more densely linked than expected based on their degree alone, i.e. forming a central rich club. Extending recent findings of rich club topology in the cat and human brain, this report presents evidence for the existence of rich club organization in the cerebral cortex of a non-human primate, the macaque monkey, based on a connectivity data set representing a collation of numerous tract tracing studies. Rich club regions comprise portions of prefrontal, parietal, temporal and insular cortex and are widely distributed across network communities. An analysis of network motifs reveals that rich club regions tend to form star-like configurations, indicative of their central embedding within sets of nodes. In addition, rich club nodes and edges participate in a large number of short paths across the network, and thus contribute disproportionately to global communication. As rich club regions tend to attract and disperse communication paths, many of the paths follow a characteristic pattern of first increasing and then decreasing node degree. Finally, the existence of non-reciprocal projections imposes a net directional flow of paths into and out of the rich club, with some regions preferentially attracting and others dispersing signals. Overall, the demonstration of rich club organization in a non-human primate contributes to our understanding of the network principles underlying neural connectivity in the mammalian brain, and further supports the hypothesis that rich club regions and connections have a central role in global brain communication.
Disease spreading through human travel networks has been a topic of great interest in recent years, as witnessed during outbreaks of influenza A (H1N1) or SARS pandemics. One way to stop spreading over the airline network are travel restrictions for major airports or network hubs based on the total number of passengers of an airport. Here, we test alternative strategies using edge removal, cancelling targeted flight connections rather than restricting traffic for network hubs, for controlling spreading over the airline network. We employ a SEIR metapopulation model that takes into account the population of cities, simulates infection within cities and across the network of the top 500 airports, and tests different flight cancellation methods for limiting the course of infection. The time required to spread an infection globally, as simulated by a stochastic global spreading model was used to rank the candidate control strategies. The model includes both local spreading dynamics at the level of populations and long-range connectivity obtained from real global airline travel data. Simulated spreading in this network showed that spreading infected 37% less individuals after cancelling a quarter of flight connections between cities, as selected by betweenness centrality. The alternative strategy of closing down whole airports causing the same number of cancelled connections only reduced infections by 18%. In conclusion, selecting highly ranked single connections between cities for cancellation was more effective, resulting in fewer individuals infected with influenza, compared to shutting down whole airports. It is also a more efficient strategy, affecting fewer passengers while producing the same reduction in infections.
We study an adaptive statistical approach to analyze brain networks represented by brain connection matrices of interregional connectivity (connectomes). Our approach is at a middle level between a global analysis and single connections analysis by considering subnetworks of the global brain network. These subnetworks represent either the inter-connectivity between two brain anatomical regions or by the intra-connectivity within the same brain anatomical region. An appropriate summary statistic, that characterizes a meaningful feature of the subnetwork, is evaluated. Based on this summary statistic, a statistical test is performed to derive the corresponding p-value. The reformulation of the problem in this way reduces the number of statistical tests in an orderly fashion based on our understanding of the problem. Considering the global testing problem, the p-values are corrected to control the rate of false discoveries. Finally, the procedure is followed by a local investigation within the significant subnetworks. We contrast this strategy with the one based on the individual measures in terms of power. We show that this strategy has a great potential, in particular in cases where the subnetworks are well defined and the summary statistics are properly chosen. As an application example, we compare structural brain connection matrices of two groups of subjects with a 22q11.2 deletion syndrome, distinguished by their IQ scores.
Graph-based computational network analysis has proven a powerful tool to quantitatively characterize functional architectures of the brain. However, the test-retest (TRT) reliability of graph metrics of functional networks has not been systematically examined. Here, we investigated TRT reliability of topological metrics of functional brain networks derived from resting-state functional magnetic resonance imaging data. Specifically, we evaluated both short-term (<1 hour apart) and long-term (>5 months apart) TRT reliability for 12 global and 6 local nodal network metrics. We found that reliability of global network metrics was overall low, threshold-sensitive and dependent on several factors of scanning time interval (TI, long-term>short-term), network membership (NM, networks excluding negative correlations>networks including negative correlations) and network type (NT, binarized networks>weighted networks). The dependence was modulated by another factor of node definition (ND) strategy. The local nodal reliability exhibited large variability across nodal metrics and a spatially heterogeneous distribution. Nodal degree was the most reliable metric and varied the least across the factors above. Hub regions in association and limbic/paralimbic cortices showed moderate TRT reliability. Importantly, nodal reliability was robust to above-mentioned four factors. Simulation analysis revealed that global network metrics were extremely sensitive (but varying degrees) to noise in functional connectivity and weighted networks generated numerically more reliable results in compared with binarized networks. For nodal network metrics, they showed high resistance to noise in functional connectivity and no NT related differences were found in the resistance. These findings provide important implications on how to choose reliable analytical schemes and network metrics of interest.
We describe a novel mechanism that mediates the rapid and selective pattern formation of neuronal network activity in response to changing correlations of sub-threshold level input. The mechanism is based on the classical resonance and experimentally observed phenomena that the resonance frequency of a neuron shifts as a function of membrane depolarization. As the neurons receive varying sub-threshold input, their natural frequency is shifted in and out of its resonance range. In response, the neuron fires a sequence of action potentials, corresponding to the specific values of signal currents, in a highly organized manner. We show that this mechanism provides for the selective activation and phase locking of the cells in the network, underlying input-correlated spatio-temporal pattern formation, and could be the basis for reliable spike-timing dependent plasticity. We compare the selectivity and efficiency of this pattern formation to a supra-threshold network activation and a non-resonating network/neuron model to demonstrate that the resonance mechanism is the most effective. Finally we show that this process might be the basis of the phase precession phenomenon observed during firing of hippocampal place cells, and that it may underlie the active switching of neuronal networks to locking at various frequencies.
Generalized tonic-clonic seizures (GTCS) are characterized by unresponsiveness and convulsions, which cause complete loss of consciousness. Many recent studies have found that the ictal alterations in brain activity of the GTCS epilepsy patients are focally involved in some brain regions, including thalamus, upper brainstem, medial prefrontal cortex, posterior midbrain regions, and lateral parietal cortex. Notably, many of these affected brain regions are the same and overlap considerably with the components of the so-called default mode network (DMN). Here, we hypothesize that the brain activity of the DMN of the GTCS epilepsy patients are different from normal controls, even in the resting state. To test this hypothesis, we compared the DMN of the GTCS epilepsy patients and the controls using the resting state functional magnetic resonance imaging. Thirteen brain areas in the DMN were extracted, and a complete undirected weighted graph was used to model the DMN for each participant. When directly comparing the edges of the graph, we found significant decreased functional connectivities within the DMN of the GTCS epilepsy patients comparing to the controls. As for the nodes of the graph, we found that the degree of some brain areas within the DMN was significantly reduced in the GTCS epilepsy patients, including the anterior medial prefrontal cortex, the bilateral superior frontal cortex, and the posterior cingulate cortex. Then we investigated into possible mechanisms of how GTCS epilepsy could cause the reduction of the functional integrations of DMN. We suggested the damaged functional integrations of the DMN in the GTCS epilepsy patients even during the resting state, which could help to understand the neural correlations of the impaired consciousness of GTCS epilepsy patients.
Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs—a combination of local network features. One technique to identify single node-motifs has been presented by Costa et al. (L. D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett., 87, 1, 2009). Here, we first suggest improvements to the method including how its parameters can be determined automatically. Such automatic routines make high-throughput studies of many networks feasible. Second, the new routines are validated in different network-series. Third, we provide an example of how the method can be used to analyse network time-series. In conclusion, we provide a robust method for systematically discovering and classifying characteristic nodes of a network. In contrast to classical motif analysis, our approach can identify individual components (here: nodes) that are specific to a network. Such special nodes, as hubs before, might be found to play critical roles in real-world networks.
The developmental mechanisms by which the network organization of the adult cortex is established are incompletely understood. Here we report on empirical data on the development of connections in hamster isocortex and use these data to parameterize a network model of early cortical connectivity. Using anterograde tracers at a series of postnatal ages, we investigate the growth of connections in the early cortical sheet and systematically map initial axon extension from sites in anterior (motor), middle (somatosensory) and posterior (visual) cortex. As a general rule, developing axons extend from all sites to cover relatively large portions of the cortical field that include multiple cortical areas. From all sites, outgrowth is anisotropic, covering a greater distance along the medial/lateral axis than along the anterior/posterior axis. These observations are summarized as 2-dimensional probability distributions of axon terminal sites over the cortical sheet. Our network model consists of nodes, representing parcels of cortex, embedded in 2-dimensional space. Network nodes are connected via directed edges, representing axons, drawn according to the empirically derived anisotropic probability distribution. The networks generated are described by a number of graph theoretic measurements including graph efficiency, node betweenness centrality and average shortest path length. To determine if connectional anisotropy helps reduce the total volume occupied by axons, we define and measure a simple metric for the extra volume required by axons crossing. We investigate the impact of different levels of anisotropy on network structure and volume. The empirically observed level of anisotropy suggests a good trade-off between volume reduction and maintenance of both network efficiency and robustness. Future work will test the model's predictions for connectivity in larger cortices to gain insight into how the regulation of axonal outgrowth may have evolved to achieve efficient and economical connectivity in larger brains.
The nematode Caenorhabditis elegans, with information on neural connectivity, three-dimensional position and cell linage, provides a unique system for understanding the development of neural networks. Although C. elegans has been widely studied in the past, we present the first statistical study from a developmental perspective, with findings that raise interesting suggestions on the establishment of long-distance connections and network hubs. Here, we analyze the neuro-development for temporal and spatial features, using birth times of neurons and their three-dimensional positions. Comparisons of growth in C. elegans with random spatial network growth highlight two findings relevant to neural network development. First, most neurons which are linked by long-distance connections are born around the same time and early on, suggesting the possibility of early contact or interaction between connected neurons during development. Second, early-born neurons are more highly connected (tendency to form hubs) than later-born neurons. This indicates that the longer time frame available to them might underlie high connectivity. Both outcomes are not observed for random connection formation. The study finds that around one-third of electrically coupled long-range connections are late forming, raising the question of what mechanisms are involved in ensuring their accuracy, particularly in light of the extremely invariant connectivity observed in C. elegans. In conclusion, the sequence of neural network development highlights the possibility of early contact or interaction in securing long-distance and high-degree connectivity.
Long-distance connections are crucial for information processing in neural systems, and changes in long-distance connectivity have been shown for many brain diseases ranging from Alzheimer's to schizophrenia. How do long-distance connections develop? Traditionally, connections can be formed over long distances using guidance cues for steering axonal growth. Subsequently, other connections can follow those pioneer axons to a target location. Alternatively, two neurons can establish a connection early on, which turns into a long-distance connection as the neural system grows. However, the relative contribution of both mechanisms previously remained unclear. Here, we study long-distance connection development in the neuronal network of the roundworm C. elegans. We find that most neurons that are connected by a long-distance connection could interact and establish contact early on. This suggests that early formation could be an influential factor for establishing long-distance connectivity, with a hypothetical role in neuronal wiring accuracy. Reducing the need for axonal guidance is also likely to reduce metabolic costs during development. We also find that highly-connected neurons (hubs) are born early on, potentially giving them more time to host and establish connections. Therefore, neuron birth times can be an important developmental factor for the spatial and topological properties of neural circuits.
Human brain networks can be characterized at different temporal or spatial scales given by the age of the subject or the spatial resolution of the neuroimaging method. Integration of data across scales can only be successful if the combined networks show a similar architecture. One way to compare networks is to look at spatial features, based on fiber length, and topological features of individual nodes where outlier nodes form single node motifs whose frequency yields a fingerprint of the network. Here, we observe how characteristic single node motifs change over age (12–23 years) and network size (414, 813, and 1615 nodes) for diffusion tensor imaging structural connectivity in healthy human subjects. First, we find the number and diversity of motifs in a network to be strongly correlated. Second, comparing different scales, the number and diversity of motifs varied across the temporal (subject age) and spatial (network resolution) scale: certain motifs might only occur at one spatial scale or for a certain age range. Third, regions of interest which show one motif at a lower resolution may show a range of motifs at a higher resolution which may or may not include the original motif at the lower resolution. Therefore, both the type and localization of motifs differ for different spatial resolutions. Our results also indicate that spatial resolution has a higher effect on topological measures whereas spatial measures, based on fiber lengths, remain more comparable between resolutions. Therefore, spatial resolution is crucial when comparing characteristic node fingerprints given by topological and spatial network features. As node motifs are based on topological and spatial properties of brain connectivity networks, these conclusions are also relevant to other studies using connectome analysis.
network analysis; network motifs; structural connectivity; human
Two previous articles proposed an explicit model of how the brain processes information by its organization of synaptic connections. The family of logic circuits was shown to generate neural correlates of complex psychophysical phenomena in different sensory systems.
Here it is shown that the most cost-effective architectures for these networks produce correlates of electrophysiological brain phenomena and predict major aspects of the anatomical structure and physiological organization of the neocortex. The logic circuits are markedly efficient in several respects and provide the foundation for all of the brain's combinational processing of information.
At the local level, these networks account for much of the physical structure of the neocortex as well its organization of synaptic connections. Electronic implementations of the logic circuits may be more efficient than current electronic logic arrays in generating both Boolean and fuzzy logic.
An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable regimes of network activation, typically arising from a limited parameter range. In this range of limited sustained activity (LSA), the activity of neural populations in the network persists between the extremes of either quickly dying out or activating the whole network. Hierarchical modular networks were previously found to show a wider parameter range for LSA than random or small-world networks not possessing hierarchical organization or multiple modules. Here we explored how variation in the number of hierarchical levels and modules per level influenced network dynamics and occurrence of LSA. We tested hierarchical configurations of different network sizes, approximating the large-scale networks linking cortical columns in one hemisphere of the rat, cat, or macaque monkey brain. Scaling of the network size affected the number of hierarchical levels and modules in the optimal networks, also depending on whether global edge density or the numbers of connections per node were kept constant. For constant edge density, only few network configurations, possessing an intermediate number of levels and a large number of modules, led to a large range of LSA independent of brain size. For a constant number of node connections, there was a trend for optimal configurations in larger-size networks to possess a larger number of hierarchical levels or more modules. These results may help to explain the trend to greater network complexity apparent in larger brains and may indicate that this complexity is required for maintaining stable levels of neural activation.
modularity; functional criticality; brain connectivity; neural dynamics; neural networks; cerebral cortex
In the rodent hippocampus, a phase precession phenomena of place cell firing with the local field potential (LFP) theta is called “theta phase precession” and is considered to contribute to memory formation with spike time dependent plasticity (STDP). On the other hand, in the primate hippocampus, the existence of theta phase precession is unclear. Our computational studies have demonstrated that theta phase precession dynamics could contribute to primate–hippocampal dependent memory formation, such as object–place association memory. In this paper, we evaluate human theta phase precession by using a theory–experiment combined analysis. Human memory recall of object–place associations was analyzed by an individual hippocampal network simulated by theta phase precession dynamics of human eye movement and EEG data during memory encoding. It was found that the computational recall of the resultant network is significantly correlated with human memory recall performance, while other computational predictors without theta phase precession are not significantly correlated with subsequent memory recall. Moreover the correlation is larger than the correlation between human recall and traditional experimental predictors. These results indicate that theta phase precession dynamics are necessary for the better prediction of human recall performance with eye movement and EEG data. In this analysis, theta phase precession dynamics appear useful for the extraction of memory-dependent components from the spatio–temporal pattern of eye movement and EEG data as an associative network. Theta phase precession may be a common neural dynamic between rodents and humans for the formation of environmental memories.
Disease spreading through human travel networks has been a topic of great interest in recent years, such as with swine inﬂuenza or SARS pandemics.
Most studies have proposed removing highly connected nodes (hubs) to control spreading. Here, we test alternative strategies using edge removal (ﬂight cancellation) for spreading over the airline network. Flight cancellation was more efﬁcient than shutting down whole airports: spreading took 81% longer if solely selected ﬂights were removed, compared to a 52% reduction when entire airports were shutdown, affecting the same number of ﬂights.