Dementia. Dementia, which is most frequently due to AD, is one of the major health problems in the ageing population, and this demands a multidisciplinary approach44. Currently, the exact cause of AD is unknown, and no effective treatment exists. The development of such treatments would require a better knowledge of the aetiology and pathophysiology, as well as effective diagnostic tools and biomarkers to identify the disease at an early phase, when treatment is most likely to be effective.

Graph theoretical analysis of structural and functional brain networks in AD has been pursued mainly to gain a better understanding of the pathophysiological processes, and to develop biomarkers for early diagnosis and for monitoring the effects of treatment. More recently, network analysis has also been applied, with similar objectives, to related neurodegenerative disorders, such as frontotemporal dementia (FTD) and Parkinson's disease (PD)45,46,47,48. Many reviews of network studies of these neurodegenerative disorders are available4,10,11,13,14,49,50,51,52,53. However, there is still considerable controversy in the literature on the exact nature of network changes in dementia, which can be explained to some extent by differences in methodological aspects14,54. Here, I review the most salient studies in an attempt to address the following three questions. First, what network changes occur in AD and AD-related disorders? Second, can these network changes be explained in terms of underlying mechanisms? And third, what could be the clinical usefulness of a network perspective in dementia?

AD is often considered to be a 'disconnection syndrome' (Ref. 55). This view suggests that a loss of neurons and their connections will interfere with the structural and functional connections between neurons and macroscopic brain regions, and that this will give rise to clinical symptoms — in particular, cognitive and behavioural deficits. However, results from network studies suggest that this view may be too simplistic, as a network is more than the sum of its connections4. Although a loss of structural and functional connections has been reported in several studies56,57,58, there are also indications of increased connectivity in AD59,60 (Fig. 3). One might expect that this mixture of increased and decreased connectivity would give rise to changes in network organization.

Figure 3: Network changes in Alzheimer's disease. a | The top left panel summarizes changes in local connectivity in individuals with Alzheimer's disease (AD) as reported in four studies (dorsal view). Continuous lines indicate higher connectivity in AD compared to controls; dashed lines indicate lower connectivity in AD compared to controls. Circle diameter corresponds to the number of studies that have reported local connectivity differences between AD and controls. b | An overview of the anatomical regions that have a hub role in healthy controls (orange) or in AD (blue). Circle diameter corresponds to the number of studies that have reported the hub status of a region. Hubs that were reported in control networks, but not in AD networks, correspond to the regions that typically show AD pathology. These associative regions — in the temporal, parietal and frontal cortices — link to other cortical areas through long-range corticocortical connections. ANG, angular gyrus; CalcF, calcarine fissure; CING, cingulum; CUN, cuneus; dSFG, dorsal superior frontal gyrus; IFG, inferior frontal gyrus; INS, insula; IPL, inferior parietal lobe; ITG, inferior temporal gyrus; LG, lingual gyrus; MFG, medial frontal gyrus; MOG, medial occipital gyrus; mSFG, medial superior frontal gyrus; MTG, medial temporal gyrus; OlfG, olfactory gyrus; OrbFG, orbitofrontal gyrus; OTG, occipitotemporal gyrus; ParaHG, parahippocampal gyrus; PreC, precingulum; PreCG, precingulate gyrus; SMG, supramarginal gyrus; SOG, superior occipital gyrus; SPL, superior parietal lobe; STG, superior temporal gyrus; STpole, superior temporal pole. Reprinted from Neurobiol. Aging, 34, Tijms, B. M., Wink, A. M., de Haan, W., van der Flier, W. M., Stam, C. J., Scheltens, P. & Barkhof, F., Alzheimer's disease: connecting findings from graph theoretical studies of brain networks, 2023–2036, Copyright (2013), with permission from Elsevier14. Full size image Download PowerPoint slide

The local connectivity of brain networks is probably best captured by the clustering coefficient or the related measure of local efficiency (Box 2). Many studies have reported a lower clustering coefficient or reduced local efficiency in AD45,46,47,56,61,62,63,64,65,66,67,68,69. This result has been obtained with various imaging techniques, including MRI tractography, MRI grey-matter network assessment, electroencephalography (EEG), magnetoencephalography (MEG) and positron emission tomography (PET). However, as mentioned above, an increase in local connectivity has also been reported58,59,70,71,72. Interestingly, studies that report increased local connectivity in AD often used different types of imaging techniques, such as group-level cortical thickness correlations and functional MRI (fMRI)58,59,70,72,73. This suggests that differences in the imaging technology used may greatly influence the assessment of local connectivity. Furthermore, methodological aspects of graph theoretical analysis — such as the use of weighted or unweighted networks, or the thresholding and normalization of graph measures — may have a role (Box 3). It is important to note that studies that used normalized measures more often reported a decrease of clustering and local efficiency in AD14,64,65.

The clustering coefficient and the local efficiency mainly capture local connectivity, whereas measures of the global efficiency and the average shortest path length reflect long-distance connections, which are probably supported by large commissural and association fibres. These long-distance connections are of special interest in view of the level of integration in large-scale networks. A loss of long-distance structural and functional connections — as reflected by an increased average path length or decreased global efficiency — has been reported in AD and in FTD in several studies, using a variety of imaging techniques46,59,62,70,74. However, a shorter path length has also been reported in AD and in PD14,45,47,60,64,65,66,69,72. Here, an important point to keep in mind is that one should distinguish between absolute and normalized path length. A decrease in normalized path length only implies that the network topology is closer to that of a random network; it does not imply that the absolute path length is shorter. This interpretation is supported by the observation that in EEG and MEG studies of AD and PD the use of normalized path length often resulted in lower values (indicating more 'random' networks) for the patient group45,64,65,66. The imaging technique itself may also be relevant. Increased path length in certain disorders has been reported in studies using group-level cortical thickness correlations, MRI tractography and fMRI46,59,62,70,73. However, even using a single imaging technology, such as fMRI, opposite changes in path length have been reported46,60,72,73. This state of affairs is frustrating, particularly in view of the fact that path length has been shown to correlate very well with cognitive function, both in healthy subjects and in patients with dementia39,40,41,61,63. This stresses the need to develop new tools that can characterize brain-network topology in an unbiased way, such that a meaningful comparison between groups may become possible. Use of the minimum spanning tree, which fixes the number of connections in the networks to be compared and enables the reconstruction of a unique minimal subnetwork on the basis of a connectivity matrix, could be a step in this direction54.

Although the results from studies that have measured clustering and path length do not show a consistent pattern of network changes in AD, other topological features seem to be more promising. Complex brain networks consist of subnetworks (or modules), which are associated with specific cognitive functions43. There is some evidence that the normal modular structure of the brain is disrupted in AD68,75,76. In particular, the parietal module seems to be affected, and an MEG study showed that both the connections within this module and the connections between this module and other modules are decreased75. A pattern of module disconnection has also been observed in studies that used MRI68,76,77. Two other interesting, but less investigated, network features are synchronizability and assortativity. Synchronizability is a measure of the stability of synchronized oscillations in a network, and can be studied using a mathematical technique called graph spectral analysis. Two EEG studies showed a decrease in synchronizability in AD, which suggests that this may be an interesting property for further study57,78. Assortativity refers to the tendency of high-degree nodes (that is, nodes with a high number of connections to other nodes) to connect to other high-degree nodes. Interestingly, assortativity is decreased in AD, but increased in FTD46,64. However, although the observations of changes in modularity, synchronizability and assortativity are promising — for instance, for the differential diagnosis of AD and FTD — they are based on only a few studies and are in need of confirmation.

One of the important messages of network theory is that nodes within a network vary widely in their relative importance, and this has consequences for their normal function, as well as for their vulnerability to pathogenic influences. Many studies have investigated measures of node centrality — such as maximum degree, eigenvector centrality or betweenness centrality — in structural and functional networks in dementia. Almost all studies report a decrease in node centrality in AD, particularly in brain regions that can be considered higher-order association areas, such as the temporal lobe, medial parietal, posterior and anterior cingulate, and medial frontal areas45,46,57,62,68,69,70,79. Few studies report an increase of centrality in AD, and only in combination with a decrease of centrality in other regions. The selective damage to highly central hub nodes thus seems to be one of the most consistent features of brain-network changes in AD, as well as in FTD and PD. In the case of AD, there is a close spatial association between areas with large amounts of amyloid deposition and areas with high-degree hubs80, suggesting a possible link between amyloid pathology and hub vulnerability. Two studies that performed simulations to investigate the spatial distribution of network changes in AD59,65 concluded that highly connected hub nodes must be specifically vulnerable in AD. An extensive simulation study showed that many findings in AD may be explained by a process known as activity-dependent degeneration19. Specifically, this study showed that synaptic damage that is due to excessive neural firing starts a process that, after an early phase of oscillatory slowing and increased connectivity, results in an end stage characterized by decreased connectivity, more-random networks and selectively damaged hub nodes. This kind of hub overload and failure scenario as a putative general scenario for brain-network disturbance is discussed in more detail below.

In summary, the following picture of network changes in AD and related disorders emerges. Currently, the findings regarding some basic network features, such as clustering and path length, are not very consistent. This is likely to be due to the methodological aspects of imaging technology and network analysis. More promising results have been obtained with respect to decreased modularity, decreased synchronizability and changes in assortativity, which is decreased in AD but increased in FTD. The most consistent finding is the disruption of hub nodes, especially the highly connected brain regions in the temporal, parietal and frontal higher-order association areas. This suggests that the pathophysiological processes in AD specifically affect hub regions (Fig. 3). It is of clinical interest that many of these network changes are associated with cognitive deficits and behavioural changes57,61,62,63,68,75,81,82. In particular, as in healthy individuals, changes in path length are associated with changes in cognitive function61,63. So far, most studies of network changes in dementia have been conducted in individuals with AD, and only a few studies have been performed in patients with FTD or PD45,46,47,48. However, when more studies in different types of dementia become available, the usefulness of network analysis in differential diagnosis could be assessed. Furthermore, network analysis might be useful in therapeutic trials in AD. A good example is a study that has shown that the progressive decrease in clustering and path length in a group of patients with untreated AD could be prevented by a food supplement66.

Multiple sclerosis. MS is classic disorder of CNS white matter, although grey-matter and thalamic involvement are increasingly recognized. One might expect that damage to the heavily myelinated, long-distance white-matter tracts, and its effect on neurological — and in particular, cognitive — function could be detected in network studies. One clinical aim here is to contribute to solving the clinical radiological paradox — namely, the observation that the lesion 'load' on MRI scans does not always correlate very well with clinical symptoms.

Measurement of cortical thickness in individuals with MS has demonstrated a disruption of normal small-world topology in MS, and the strength of this disruption was found to correlate with the extent of white-matter damage83. A tractography study confirmed the decrease in the global and local efficiency of structural networks (as described above)84, including the default-mode network and several local networks in primary motor and sensory areas. Even in patients with the related, but much more localized, condition neuromyelitis optica, widespread changes to structural networks could be detected, although small-worldness, normalized clustering and path length were increased85. Furthermore, the tractography study84 showed both decreases (in the default-mode network as well as in sensorimotor and visual systems) and increases in node centrality in different brain regions (in orbital parts of the superior-, middle-frontal and fusiform gyri), which is compatible with a reorganization of brain networks.

An MEG study showed increased functional connectivity in the theta, lower alpha and beta bands, and decreased functional connectivity in the upper alpha band in individuals with MS compared with healthy controls37. In addition, functional networks in the lower alpha band had a more regular topology, and changes in normalized clustering were associated with impaired cognition. Remarkably, these effects were greater in male patients than in female patients37. A second MEG study investigated networks in source space by using a connectivity measure that was unbiased by volume conduction, and by using either resting-state network analysis or a minimum spanning tree analysis86,87. Compared with healthy controls, individuals with MS had functional networks that were more integrated (that is, more tightly functionally connected) in the theta band and less integrated in the alpha and beta bands. A disruption of hierarchical network organization in the upper alpha band was associated with impaired cognition, whereas disturbed beta band connectivity of the default-mode network was associated with both impaired cognition and motor deficits86. The importance of using a proper measure to assess EEG functional connectivity was revealed in a study of 308 individuals with MS who were divided into cognitively impaired and cognitively unimpaired subgroups88. This study provided evidence for a shift from global to local connectivity in cognitively impaired patients, but not in cognitively unimpaired patients; however, these results were dependent on the specific synchronization measure that was used. Finally, a resting-state fMRI study found decreases in functional connectivity, which correlated with cognitive impairment, in male patients with MS but not in female patients36.

In summary, graph theoretical studies of individuals with MS suggest that there are widespread changes in structural and functional brain networks, with global integration — which is often dependent on the default-mode network and hub structures — being especially affected. Such network changes are related to white-matter pathology84, as well as to clinical and cognitive deficits84,87,88. Thus, these changes may contribute to understanding the relationship between the lesion load that is visible in MRI scans and the clinical symptoms of this disorder.

Traumatic brain injury. TBI can give rise to diffuse axonal injury, which can interfere with normal communication between brain areas. In view of this, the study of structural and functional brain networks has become an important approach for understanding cognitive dysfunction and late encephalopathy in TBI13.

An MRI tractography study of 17 individuals with TBI and 12 control participants reported a widespread loss of structural connections in the patients with TBI89. This was associated with lower local efficiency, increased path length and increased betweenness centrality. Studies of functional networks in TBI have also demonstrated an extensive disruption of connections and network reorganization. For example, in patients who are in a minimally conscious state following TBI, the loss of connectivity (as assessed by EEG) occurs in all frequency bands90. At the other extreme, patients with very mild TBI only show disturbances in EEG-network topology in the theta and alpha bands during performance of an episodic-memory task91.

Most studies of functional network organization in TBI have used resting-state fMRI. Often, fMRI studies report a loss of connectivity, in particular with respect to long-distance connections92,93,94. This loss is typically associated with a disturbance of the normal small-world topology — reflected in particular by an increase in path length — which may recover to some extent95,96. One fMRI study reported an increase in connectivity during a motor-switching task in patients with TBI97. The same researchers also reported a lack of correspondence between the structural and functional changes to the brain networks98. TBI can also be associated with changes in the modular structure of functional brain networks92,95. In a study of individuals who sustained TBIs that were due to shock blast, the main network abnormality concerned the connectivity between modules, as reflected by a decrease in the so-called 'participation coefficient' (Ref. 95). Interestingly, a similar pattern of disturbed intermodular communication has also been observed in AD75. Another feature of TBI is the selective damage of hub-like structures in the association cortices and the default-mode network94,96. An important study that compared individuals with severely impaired consciousness (following a range of acute medical events) with healthy subjects showed that although the groups had similar overall network characteristics96, the spatial distribution of the hub nodes over the network was clearly different in the individuals with impaired consciousness. Such hub redistribution — from areas such as the precuneus and fusiform gyrus in controls, to areas such as the angular gyrus in patients with TBI — could be a late signature of post-trauma network reorganization.

These studies suggest that TBI can result in a loss of (especially long-distance) structural and functional connectivity, probably via the mechanism of diffuse axonal injury. This loss of connectivity is accompanied by network reorganization that is characterized by increased path length, abnormal modularity and a redistribution of hubs.

Epilepsy. Epilepsy, which is defined as a tendency towards recurrent unprovoked seizures, is one of the most prevalent neurological conditions worldwide. It presents one of the most interesting applications of modern network analysis, as here, more than in other disorders, network analysis is very close to the stage at which new treatment approaches, particularly surgery, can be realized99,100,101,102,103. Indeed, the classic concept of an 'epileptic focus' is being replaced by that of an 'epileptic network', and graph theory has had a major role in pointing out the key properties of the most important elements of this network.

In patients with temporal lobe epilepsy (TLE), structural networks based on cortical thickness correlations have increased clustering, a longer path length, an altered hub distribution and a higher sensitivity to attacks that are targeted specifically at hubs104. Importantly, these network abnormalities increased over time, and more severe abnormalities were associated with a worse outcome of epilepsy surgery104. MRI tractography studies have confirmed the presence of widespread abnormalities in structural networks105,106,107,108,109, not only in focal epilepsy, but also in generalized types of epilepsy109. A general pattern that is observed in these studies includes changes in local connectivity in combination with disruptions to long-distance connections that often involve important hub regions in the default-mode network107,108. Furthermore, the extent of network changes often correlates with the severity of cognitive disturbances, the outcome of epilepsy surgery and the disease duration106,108,109.

Not surprisingly, the focus of network studies of epilepsy has been on functional networks, particularly those derived from EEG and MEG recordings. Studies that have assessed network changes that occur during the ictal state have produced the most consistent results. One early study assessed functional networks that were derived from depth-electrode recordings that were taken before, during and after temporal lobe seizures, and reported a more regular topology, with high clustering and long path length during the ictal state110. Studies that used intracranial recordings also reported a shift towards a more regular network topology111,112,113. Such ictal network regularization was confirmed in scalp EEG and MEG recordings during absence seizures with generalized 3 Hz spike–wave discharges114,115. Although there is support for the concept of pathological ictal network regularization, it is not clear whether interictal and preictal networks also have an abnormal topology. I therefore discuss studies on interictal network topology in the context of two questions. First, are interictal networks abnormally regular, like ictal networks are? And second, what is the role of hub nodes in the spread of seizure activity?

Regarding the first question, some studies show that EEG- or MEG-based functional brain networks of individuals with epilepsy in an interictal state are abnormally regular compared with those of healthy subjects116,117. Such interictal network regularization has also been observed using depth-electrode recordings in individuals with TLE118. One study suggested that in the interictal state, regularization might occur in the theta band, whereas alpha band networks are abnormally random119. However, in another study, interictal network randomness increased with disease duration in individuals with TLE120. Other studies have also shown an association between excessive synchronization in the theta band and epilepsy121,122,123. In general, the interictal network topology in individuals with epilepsy seems to have shifted from the small-world organization that is seen in healthy subjects towards the excessive regularity that is observed during seizures. Unfortunately, this does not yet imply that interictal network topology can be used to predict when a seizure will occur124.

The second question regarding interictal network topology is whether hubs are important for the propensity of seizures to spread through the brain125. Functional brain networks can be derived in an unbiased way using a minimum spanning tree approach126. One study that used a minimum spanning tree analysis of acute corticography recordings from individuals with TLE to identify hub nodes (on the basis of several criteria) suggested a possible association between node centrality and surgical outcome127. In a prospective study in individuals with both brain tumours and epilepsy, the networks of individuals who became seizure-free after surgery were more integrated and showed higher centrality at follow-up than the networks of patients who were not seizure-free after surgery128. In another study, surgical removal of the tissue that corresponded to network nodes with high betweenness centrality was associated with a more favourable outcome129. Additional studies also suggest the importance of hub-like structures, particularly in high-frequency ranges, for the spreading of seizure activity130,131,132. Indeed, hub-like features identified in EEG recordings can be valuable for predicting whether children will develop epilepsy after an initial seizure-like event133. Two studies compared the phase synchronization and node centrality of functional networks exhibiting high-frequency oscillations (HFOs), which are an important feature of epileptogenic tissue134,135. Somewhat surprisingly, the number of HFOs was inversely correlated with node centrality in the theta band135. This finding suggests that areas with HFOs and areas with high-degree nodes may not be the same, and could represent two different and perhaps even spatially separated components of the epileptogenic zone.

The pattern of increased local connectivity and decreased global connectivity (features that are typical of more regular networks) that is observed in structural MRI studies of individuals with TLE has been confirmed in resting-state fMRI studies136,137. The connectivity of the default-mode network is diminished both in individuals with TLE and in individuals with generalized epilepsy. Changes in fMRI-based functional networks are also associated with impaired cognition in such patients. For example, a study in individuals with cryptogenic localization-related epilepsy showed an association between lower clustering coefficients and increased cognitive impairment138, and stronger modularity was associated with more-impaired cognition in children with frontal lobe epilepsy139. These observations are in line with a previous report of abnormal modularity in individuals with absence epilepsy116.

Some recent studies have combined the use of fMRI with structural MRI in the same subjects140,141,142. One such study found reduced coupling between structural, tractography-based and functional networks in individuals with idiopathic generalized epilepsy, with the strength of hub nodes and the default-mode network connectivity being diminished in particular142. In contrast with this finding, a study that related fMRI-based networks with cortical thickness-based networks showed increased coupling between functional and structural networks140. In a study in children with frontal lobe epilepsy, fMRI-derived functional networks showed the well-known pattern of increased clustering, longer path length and higher modularity, but structural networks were not different between patients and healthy controls141. Moreover, the increased modularity of structural networks in these individuals was associated with more-severe cognitive impairment.

Several patterns emerge from network studies in epilepsy. In both focal and generalized epilepsy, there is a widespread involvement of structural and functional brain networks. MRI studies show that epilepsy is characterized by a tendency towards increased local connectivity and decreased global, long-distance connectivity that affect, in particular, the default-mode network and hubs in association areas. These changes are associated with cognitive disturbances, longer disease duration and poor surgical outcome. During seizures, functional brain networks display a pathological regularization. Similar changes can be observed, to a lesser extent, in the interictal state. Furthermore, the strength of hub nodes in functional networks is associated with the outcome of epilepsy surgery and has diagnostic value.

Is it possible to sketch the outlines of a 'network theory of epilepsy' on the basis of these findings? Here we should distinguish between the local and the global levels. At the local level, epilepsy is characterized by a small brain area with abnormally increased excitability (the epileptogenic zone and the origin of HFOs), increased structural connectivity (possibly the result of damage and rewiring) and one or more highly connected hubs. The local components may be responsible for the increased activity, synchronization and network regularity in the interictal state. Only if the activation exceeds a critical threshold will activity spread — through general hub-like structures such as the default-mode network — to the rest of the network, and this then results in a generalized seizure and a transiently hyper-regular functional network. If this process occurs repeatedly, long-distance connections and general hubs will become damaged, resulting in a loss of long-distance connectivity and, eventually, in cognitive dysfunction. Understanding the network aspects of epilepsy may lead to new approaches to epilepsy treatment, for instance in the context of epilepsy surgery. A hypothetical scenario for such an application is depicted in Fig. 4.