blood - oxygen - level - dependent ( bold ) functional magnetic 
 resonance imaging ( fmri ) is an imaging technique that makes it possible to 
 dynamically and noninvasively track metabolic and hemodynamic changes in the 
 brain [ 1 , 2 ]
. the 
 early developments of bold fmri data analysis have mostly relied on a method 
 called general linear model ( glm ) , whose objective is to pinpoint the differential 
 involvement of certain regions during various tasks [ 35 ] . 

voxel clusters that exhibited such a behavior are declared  activated  and 
 gathered into a so - called activation map that provides the output of the glm 
 approach ; each map represents all regions that are significantly correlated 
 with the stimulus time course .
glm - based methods have been extensively used in 
 order to extract regions in a wide variety of conditions ( see , e.g. ,   for a review of activation 
 studies related to the premotor cortex ) .
the glm , 
 however , does not properly render the brain 's intricate organization , which is 
 believed to be based on two major principles : segregation and integration [ 7 , 8 ] . according to these 
 two principles , functional tasks are performed by specific collections of brain 
 regions , also called networks , that are anatomically connected and can engage 
 in complex interactions [ 911 ] .
even though the bold contrast is only remotely related 
 to neuronal activity , it was first hypothesized , and then evidenced , that this 
 imaging modality is able to reflect , at least to some extent , the strong 
 constraints imposed on the brain by segregation and integration .
first , studies showed that brain regions could still be correlated 
 at rest , hinting for the existence of functional brain networks that could still 
 be present and imaged even when no task was explicitly required from the 
 subject [ 12 , 13 ] . 

network investigation also started with a closer examination of the 
  baseline ,  that is , the signal measured when a subject is in the  rest  condition 
 of a protocol , between two task conditions .
this approach was justified from the fact that , from an 
 energetic perspective , the brain uses a significant part of the body 's energy , 
 independently of the presence or absence of a  task 
[ 15 , 16 ] . as methods of 
 increasing complexity were developed and validated , the objective of many 
 methodological developments shifted from glm - related procedures to methods that 
 were able to extract networks from bold fmri data .
this paper is 
 an attempt to review the latest advances in investigation of extended 
 large - scale networks in fmri from a methodological perspective , as well as the 
 networks that have been found using these methods .
this new methodology , if 
 confirmed , has very deep implications in terms of methods that should be 
 developed , and we discuss some of the issues that such methods will have to 
 deal with in order to provide reliable and useful results .
an extended large - scale functional brain network may 
 be defined as a ( potentially large ) number of segregated regions ( potentially 
 spread over the whole brain ) that interact in order to execute a coherent task . 
 while bressler and tognoli   mostly consider 
  high - level brain functions of which cognition is comprised , 
it is important 
 to emphasize the fact that about any function that the brain is able to process 
 is likely to have a network representation ( see , e.g. , section 4 for a 
 description of some low - level brain functions , such as vision and audition 
 processing ) .
first , they are widely distributed over 
 the brain . as a consequence of the segregation principle ,
it is hypothesized 
 that they can be broken down into small brain regions , coined  nodes  by mesulam ,  units  by marrelec et al . , and  local cortical area 
 networks  by bressler and tognoli , each 
 region being characterized by a consistent functional behavior .
such nodes can 
 readily be identified in subcortical structures , which are often gathered into 
 nuclei . as to the cortex , 
 despite cytoarchitectonic features ( embodied , e.g. , by the 
 work of    brodmann   and his eponymous regions ) 
 that vary across its surface , its parcellation based on structural criteria 
 alone remains globally a challenge .
for instance , primary sensory regions ( e.g. , visual ) have 
 been localized in a quite reproducible manner ; within these regions , areas 
 responding more specifically to certain types of inputs have been successfully 
 identified ( e.g. , vertical versus horizontal lines in the primary visual 
 cortex ) .
still , even though 
 various levels of specialization can usually be observed , there is a general 
 agreement that most regions can not be unambiguously associated with one 
 specific function ( see , e.g. ,   for broca 's area ) and , in general , a region will exhibit a 
 certain level of  multifunctionality  : its contribution will not be limited to one task but will 
 be allowed to vary within a given range of functions that it is able to 
 implement . as a 
 consequence of the integration principle , large - scale networks are also 
 characterized by potentially distant regions with strong ( anatomical ) 
 connections and ( functional ) interactions .
whether top - down or bottom - up , 
 serial or parallel , connections and interactions are quintessential of 
 networks [ 18 , 24 , 25 ] . 
 anatomically , interregional connectivity is suspected to be rather sparse [ 2630 ] .
even though most connections originating from one 
 region are thought to re - enter the same region , axons are known to connect 
 regions that are far apart from each other , for example , homologue regions [ e.g. , [ 3133 ] ] .
functionally , these 
 connections have translations at all levels , from electrophysiology [ 3438 ] 
 to measures of the electromagnetic field   and of the bold signal [ 12 , 13 ] . whether coined 
  new phrenology    or 
 considered as being  beyond phrenology 
, such an approach leads to a model of brain functions in 
 which most functional tasks are subserved by functional brain networks , that is , 
 collections of specialized regions that collaborate in order to generate a 
 coherent behavior [ 11 , 36 ] . in support of this approach ,
luria   refers to three blocks : one that  regulates the energy level 
 and tone of the cortex ,  another one that is strongly implicated in 
 information processing , and a last one that is involved in higher , complex 
 tasks , such as  the formation of intentions and programs for behavior . 
first , based on the co - occurrence of functions with 
 similar features , the brain can be divided into five major  subtypes  : 
 primary sensory - motor , unimodal association , heteromodal association , 
 paralimbic , and limbic .
there are also at least five large - scale networks , each 
 dealing with a specific cognitive function : spatial awareness , language , 
 explicit memory / emotion , face - object recognition , and working memory - executive 
 function .
these networks are not isolated from one another , but interact in 
 very complex fashion , for example , through  transmodal  areas .
relying on the assumption that bold fmri is indeed 
 able to image brain networks ( see , e.g. ,   for a review of the neurophysiological substrate of 
 neuroimaging ) , two categories of methods may be identified for such studies : 
 approaches that make use of prior cognitive information and fully exploratory 
 methods .
correlational methods were historically the first ones 
 to be applied to investigate large - scale networks in fmri data analysis , in the 
 form of functional connectivity studies and functional connectivity maps [ 12 , 4147 ] .
one extracts all 
 voxels whose time courses are significantly correlated with that of the seed . 

measures other than temporal correlation have also been used , such as coherence 
 and partial coherence [ 48 , 49 ] .
selection of the seed region is a key issue in studies of functional 
 connectivity .
first , a brain region is selected according to its function 
 ( e.g. , cortical representation for hand movement , ) .
the corresponding seed is then 
 obtained from either prior anatomical knowledge or functional manipulation . 

anatomically , common approaches consist of using coordinates in a standardized 
 space ( talairach or mni ) , or 
 having an expert delineate the region on anatomical images .
functionally , the seed can be obtained 
 from an activation map , provided that the region of interest can be 
 characterized by its implication in a specific task ( e.g. , the primary motor 
 cortex in a simple movement ) [ 41 , 45 , 47 ] . as opposed to 
 effective connectivity  where gonlaves and hall   showed that results of sem analyses may vary depending on 
 the choice of the seed voxel 
robustness of functional connectivity maps with 
 regard to the selection of the seed region and its spatial extent have barely 
 been examined yet .
vincent et al .   showed 
 that , for the visual or the somatomotor network , the resulting functional 
 connectivity map was robust to the choice of the starting seed region .
many 
 other parameters ( e.g. , design , size of each region ) may have an influence on 
 the outcome of the analysis , potentially leading to different spatial 
 structures or correlation values between structures .
full exploration of a 
 whole network ( i.e. , with many regions ) would imply the recourse to several 
 successive computations of functional connectivity maps , each map being used to 
 select a region significantly correlated as seed voxel for the next step  a 
 procedure that is lengthy , complex , and whose convergence is not assured .
wang and xia   have recently proposed a method 
 to perform this exploration in only one step .
the goal of fully exploratory methods is to provide 
 data - driven approaches of large - scale network detection in which no prior 
 cognitive information is required for the methods to proceed .
a number of such 
 procedures have been proposed , most of them relying more or less closely on 
 either of the two key features of large - scale networks , namely integration and 
 segregation .
based on a similarity measure , they 
 gather voxels irrespective of their anatomical proximity ( and , hence , of 
 segregation ) into separate classes that are strongly similar to each other and 
 dissimilar from one another . for each class , the output is a map representative 
 of the class and an associated time course .
all methods have one or several 
 parameters whose tuning affects the number of classes . since each class tends 
 to gather voxels that are strongly correlated , it is often univocally 
 identified with a large - scale network .
blind approaches include methods based 
 on eigenvalue decomposition , such as principal component analysis ( pca ) [ 5355 ] , correlation 
 clustering , kendall 's 
 coefficient of concordance [ 57 , 58 ] , k - means [ 59 , 60 ] , fuzzy clustering 
 methods [ 54 , 56 ] , self - organizing map algorithms , kohonen clustering neural 
 network and fuzzy c - means , 
 hierarchical clustering [ 60 , 63 ] , 
 integration and information - theoretic quantities [ 64 , 65 ] , and spatial 
 independent component analysis ( sica ) .
while most methods provide maps that are exclusive ( a 
 voxel can only belong to one map ) , a few ( e.g. , fuzzy clustering or ica ) 
 provide an index of the plausibility for a voxel to belong to each of the 
 different classes .
most methods also provide local criteria , calling for 
 stepwise analyses , at the exception of pca and ica that use global measures 
 and , consequently , are able to perform classification in one step .
most approaches 
 mentioned in the previous paragraph have only been used a limited number of 
 time in fmri data analysis so far .
this can probably be accounted for by the 
 complexity of their algorithms , which is commensurate with the difficulty of 
 the task at hand .
outstandingly , sica has been used quite a lot recently , with 
 results that are rather promising .
regardless of its popularity , though , the 
 network interpretation of the results obtained needs to be proved beyond simple 
 criteria ( these include , e.g. , that voxels located close to each other or in 
 homologue regions tend to belong to the same class ) . for instance , for 
 pca , friston and bchel   mention that the 
 interpretation of the eigenimages in biological terms might be dubious , since 
 they could be rotated in the data space and still be a solution to the problem 
 ( but see ) .
by contrast , 
 components obtained through ica can be more easily related to known 
 physiological noises or functional processes [ 66 , 69 ] .
the methodological reasons for this success 
 are , however , still not clear , and many explanations are plausible : the 
 relevance of the assumption of spatial independence , the adequacy of the 
 underlying mixing model , the efficiency of the global criterion / one - step 
 discrimination approach , or some interesting feature of the 
 information - theoretic optimization algorithm . in any case , the fact that its 
 application simplifies the results to a maximum and produces a very limited 
 number of widespread networks , making interpretation easier , clearly plays in 
 its favor ( compare , e.g. , with [ 70 , 71 ] , or ) . its sensitivity , which 
 is much higher than that of clustering methods , might also explain its success . 

nevertheless , it must still be kept in mind that the assumptions underlying ica 
 ( perfect synchrony within a network and spatial independence between networks ) 
 impose an extreme and unrealistic case of integration .
while the simplification 
 of several time courses into one is performed only once for ica , the stepwise 
 procedures implemented by other methods essentially go through the same 
 approximation at each step , leading to an error that is probably far larger .
unlike the 
 numerous approaches to functional integration , few methods have specifically 
 sought to extract segregated regions .
some methods decrease the complexity of 
 the data by using predefined regions ( e.g. , according to the tzourio - mazoyer et al .  
approaches 
 using predefinite regions do not check that all voxels within a region exhibit 
 homogeneous bahaviors ; they merely assume that it is the case .
average signals 
 are then extracted from each region , on which any integration - based approach , 
 such as hierarchical clustering [ 71 , 72 ] , can be applied .
intuitively , many 
 clustering methods mentioned previously ( e.g. , k - means , hierarchical 
 clustering , or information - theoretic measures ) could easily be applied for the 
 purpose of detecting segregated regions by incorporating a constraint of 
 contiguity between voxels that could be merged . among these
, only the 
 information - theoretic approach explicitly takes both within- and 
 between - classes measures of similarity into account .
specifically , they optimize 
 a so - called functional clustering index ( fci ) that keeps a balance between 
 region homogeneity ( strong segregation ) and sparseness of inter - regional 
 interactions ( low integration ) [ 64 , 65]the latter constraint being hard to justify 
 from a network perspective . as to other clustering methods , as noted by goutte et al .   in accordance to huygens ' 
 formula , maximizing a measure of the internal coherence of a class ( associated 
 with segregation ) is often equivalent to minimizing the same measure of 
 coherence but computed between classes ( that could be associated with 
 integration ) . as such
, the behavior of such methods with regard to networks 
 would again lead to questioning . a tentative 
 approach to consider simultaneously segregation and integration has been 
 conducted by the large scale 
 network identification ( lsni ) method by bellec et al . .
lsni first clusters neighboring voxels 
 into small regions using a region - growing algorithm   and then selects regions that 
 exhibit a significant correlation with other distant regions .
such a procedure 
 allows to define brain functional regions and networks in a purely data - driven 
 way .
while the sensitivity of the algorithm proposed was rather low , it had the 
 great advantage to explicitly define and address the two principles of 
 functional segregation and integration .
so far , this method seems adapted for 
 individual analyses ; its extension to group studies seems limited due to the 
 subject - dependent definition of regions .
during the last decade , several brain systems have 
 been studied in fmri using functional connectivity - related approaches .
these 
 studies have revealed integrated systems , including primary systems and 
 associative networks .
exploratory approaches have also allowed to extract 
 several functional networks at once . even if all brain areas are not included 
 in a network , these networks involve many areas and constitute a possible 
 functional parcellation of the brain . the motor 
 network was the first network studied through functional connectivity 
 analyses .
reported 
 correlations in low - frequency resting - state fluctuations between left and right 
 motor areas using single - slice fast - sampled acquisitions .
this result was later 
 reproduced with multislice acquisitions where an extended motor network was 
 shown to correlate with a region in the primary motor cortex [ 44 , 47 ] .
lowe et al .   showed that other functional networks 
 could be detected using other seed regions , namely the visual network with a 
 seed around the calcarine fissure and a limbic network with a seed in the 
 amygdala .
an auditory and a language systems were later extracted in the same 
 way [ 41 , 43 ] .
other 
 networks were also studied using the seed - region functional connectivity 
 approach , such as the default - mode network [ 8386 ] , the attentional 
 networks [ 42 , 83 , 87 ] , and memory networks [ 46 , 88 ] .
more 
 recently , a larger number of functional networks were revealed using 
 exploratory methods based on ica [ 7678 ] .
even if the number of 
 extracted networks varied , their spatial organizations were reproducible across 
 studies .
for instance , all three studies just mentioned found functional 
 networks involving the same systems that were sometimes split into different 
 parts ( e.g. , left / right , rostral / caudal ) .
using group ica studies of 
 resting - state datasets [ 7678 ] , which were the most reproducible , we selected 
 seven functional networks : a motor / sensorimotor system , a visual system , an 
 auditory system , a default - mode network , a dorsal attentional network , a 
 ventral attentional network , and an executive control network .
van de ven et al .   systematically studied the 
 reproducibility of ica results on individual datasets and the results using 
 hierarchical clustering   and 
 self - organizing map algorithm ( som )   were presented on an individual level .
the results from 
 studies that provided a systematic description of all networks found are 
 reported in table 1 . 
 in figure 1 and table 2 , we also reported results from a study on a 
 population of 20 healthy subjects acquired at rest , where networks were 
 extracted using spatial ica and a hierarchical clustering approach similar to that of esposito et al . .
the 
 sensorimotor system involves at least the pre- and postcentral gyri ( including 
 the primary motor cortex and supplementary motor area ) .
the visual system 
 involves both medial striate and extrastriate regions ( calcarine sulcus and 
 lingual gyrus ) , as well as lateral occipital regions ( nonprimary visual 
 regions ) ; these two visual networks ( primary and associative ) were identified 
 separately by the three group - ica studies .
the auditory system involves 
 principally lateral superior temporal gyri , the heschl 's gyrus and insular 
 cortex .
the so - called default - mode network involves the anterior and posterior 
 cingulate cortices , the medial prefrontal cortex and lateral parietal 
 regions [ 15 , 8991 ] .
the dorsal attentional network involves lateral 
 prefrontal and dorsal partietal cortex ; these regions are involved in 
 visio - spatial control [ 42 , 92 , 93 ] .
the ventral attentional network involves inferior 
 occipito - parietal regions and inferior lateral prefrontal regions ; these regions 
 are principally involved in new item recognition [ 42 , 94 ] .
last , the executive 
 control network involves superior and middle prefrontal cortices , ventrolateral 
 prefrontal cortex and anterior cingulate gyrus .
other studies have 
 applied these exploratory approaches to extract integrated functional networks 
 from fmri datasets acquired during external stimulation [ 73 , 79 , 80 ] .
these results showed that 
 the detection   of the functional networks not directly related to the 
 stimulation were less sensitive than that without 
 external stimulation .
tracking the presence of extended large - scale networks 
 in bold fmri data raises many issues .
we have here focused on some aspects 
 related to the neurocognitive aspects of networks , their identifiability by 
 fmri , and the methodological questions raised by network analyses .
the major issue to be faced is arguably the very 
 definition of an extended large - scale brain network . indeed , even though the 
 brain is far from being fully connected , any region is eventually connected to 
 any other regions if one takes polysynaptic connections into account . 
 obviously , stating that the brain can be considered as one network is by no way 
 satisfying , no more than it is to say that each macrocolumn forms a networks by 
 itself .
the strongly hierarchical nature of the brain 's anatomical and 
 structural organization induces similar characteristics at all levels .
as the 
 brain can be decomposed in networks , each network can in turn be further 
 partitioned into subnetworks , subnetworks into subsubnetworks , and so on . 

furthermore , even though there probably is a ( potentially loose ) relationship 
 between anatomical and functional organizations , it is still unknown how 
 functional integration and segregation are coded in anatomical terms . for the 
 exact same structural organization , it has been shown that networks can be 
 observed to break down as one discriminates different sets of functional tasks 
 or behaviors with increasing precision .
for instance , the visual system can be 
 decomposed into a ventral and a dorsal stream .
these two subnetworks , albeit interacting , have very distinct 
 functions [ 42 , 92 , 96 ] .
similarly , the motor system can be further 
 separated into a cerebello - cortical and a basal - cortical loop with different 
 patterns of involvement [ 97 , 98 ] .
for instance , it has been argued that the 
 fronto - parietal network could be further partitioned into two subnetworks 
 subserving attention and working memory , respectively , , while the working memory network 
 itself could be further broken down in two , with one subnetwork mediating 
 attentional selection and another one rather underlying language functions .
for instance , 
 activation of some fronto - parietal regions is observed during different 
 cognitive tasks ; are these 
 regions transmodal or part of a subnetwork that has a specific function ? 

similarly , the insular cortex is typically a multimodal association area that 
 is not specifically activated by auditory stimuli .
however , as reported in 
 section 4 , recent papers have consistently classified it as belonging to a 
 so - called auditory system .
as evidenced by figure 1 , there are also some 
 overlapping between networks , and voxels can be simultaneously classified as 
 belonging to different networks . what is the function of such regions ?
could 
 this overlapping between networks be related to synchronization through distinct 
 frequency - bands if such 
 a phenomenon is indeed visible through fmri bold imaging ? regarding the 
 influence of a task on a network , an issue that has not received much attention 
 yet , studies have shown that networks could indeed be influenced by the 
 processing of a task , either during the task   or even after it .
it is hence not unrealistic to suspect that processing of a 
 task might also modify the very structure of some networks .
another cogent 
 question is the relationship between networks as detected by fmri data analyses 
 and those mentioned in the literature .
networks extracted from fmri are the 
 consequence of the optimization of a mathematical criterion whose link to 
 neuroscience is , at the very least , not obvious . while some results have been 
 rather successfully related to the neurocognitive literature ( e.g. , attentional 
 network ) , other results are more complex to interpret .
some networks extracted 
 seem to share commonalities with some of the subtypes 
 described by mesulam   ( e.g. , the motor network ; cf . 
 section 2 ) , while others seem to be rather 
 related to   mesulam 's neurocognitive networks 
 ( e.g. , the attentional network ) .
besides , the union of all reported networks 
 ( e.g. , by sica ) does not include the whole brain . some brain regions
globally , the criterion used for network extraction might make the methods 
 sensitive to some functions or types of connections .
for instance , top - down and 
 bottom - up influences have distinct features [ 25 , 34 , 3638 ] . 

apart from 
 these difficulties , there has also been evidence of variability across healthy 
 subjects [ 80 , 103 ] that 
 could be explained by many factors , such as development and/or age [ 104 , 105 ] , and , in general , all 
 forms of plasticity [ 106 , 107 ] .
pathologies , for example , stroke [ 108 , 109 ] or tumors [ 110113 ] , render the issue 
 even more complex .
some studies have shown that certain pathologies can have 
 network - specific effects : behavioral deficits in spatial neglects for the 
 fronto - parietal network ; 
 epilepsy   and alzheimer 's 
 disease   for the 
 default - mode network .
nonetheless , these results must be used with caution , for 
 it is not clear yet whether they truly reflect a change in neuronal properties 
 or , as , for example , in grade ii glioma , a mere modification of the metabolic 
 and vascular properties of the surrounding tissues .
use of bold fmri as a way to investigate large - scale 
 networks relies on three successive assumptions , namely , that information 
 exchanges between neurons is related to synchronies , synchronies to the bold 
 contrast , and the bold contrast to the fmri data effectively measured .
synchronies are 
 the blueprint of communication between regions [ 17 , 39 , 117120 ] and , as such , should be strongly related to large - scale networks . 

a challenging issue is to determine the exact relationship between the spatial 
 distribution and interaction pattern of regions within a large - scale network on 
 the one hand and , on the other hand , the spatial and frequential distribution 
 of oscillations .
another issue 
 is the connection between neuronal activity / synchrony and the appearance of a 
 bold signal .
while much still needs to be unraveled as to the connection 
 between neuronal synchronies and the bold signal , it now seems more and more 
 accepted that a sustained change in neuronal activity is likely to entail a 
 relative change in the bold level [ 121124 ] , even 
 though the exact relationship is expected to be rather complex .  
still , the bold 
 signal is only a fraction of the total signal that is acquired in fmri , a 
 signal that is not exempt from many kinds of artifacts [ 126128 ] . in 
 particular , some physiological processes ( e.g. , cardiac , respiratory , or 
 movement - related ) induce spurious effects that contaminate the bold signal in 
 the whole brain [ 129 , 130 ] . 

such artifacts are predominant in certain regions of the brain , such as the 
 basal arteries for cardiac activity or the interfaces between cerebrospinal 
 fluid pools and brain tissus for breathing and head movements .
some 
 network detection algorithms may hence recognize voxels influenced by the same 
 spatially structured artifact as meeting the requirement for strong temporal 
 coherence and , hence , assign them to a common structure .
this feature has been 
 successfully used by ica techniques to provide efficient noise separation and 
 removal techniques [ 66 , 131 , 132 ] . yet
, the issue arises when 
 structures induced by noise are wrongly interpreted as functional networks ; 
 their detection and removal is hence of very high importance . the fundamental 
 question , while examining spatial structures with a similar temporal behavior , 
 is  do we measure neurally induced signal or consequences of physiological 
 processes ?
 even though our understanding of 
 the potential artifacts that can contaminate the bold fmri signal improves , the 
 consequences of many potential sources of structured noise have barely been 
 mentioned , let alone investigated .
for instance , it is believed that some 
 mechanisms related to the regulation of blood flow ( e.g. , through the level of 
 co2 in the blood ) could induce 
 coherent changes in bold signal throughout the brain  giving birth to an 
 effect likely to be identified as a functional network .
in fact , such an effect 
 has been used to explain the presence of the default - mode network in fmri [ 134 , 135 ] .
now , whether these regions 
 are wrongfully classified as belonging to a common functional network because 
 their voxels are corrupted by the same artifact , or whether they are actually 
 regions that drive the physiological response is a matter that remains to be 
 solved .
we here quickly discuss 
 issues related to the choice of a model , the redundancy of fmri signals , the 
 necessity to provide both individual and group analyses , the importance of 
 result representation , and the validation of fmri results with other 
 modalities .
procedures used 
 to investigate networks are usually based on mathematical methods that have 
 been discovered independently of the field of fmri data analysis .
while it can be accepted that most methods are general enough to be applied to 
 a wide variety of problems , they still require a careful assessment of how best 
 to adapt them to the issue at hand .
we believe that the major point to cope 
 with here is  how do methods code for segregation and integration ?
does it make 
 sense ?  a relevant approach could be to try to derive out consistence 
 requirements from cognitive consideration of what an  ideal  method should be 
 able to do : quantify integration between voxels , regions , or networks using the 
 same principled measure ( such as the multiple correlation coefficient   or integration [ 7 , 137 ] ) ; 
 differentiate between direct and indirect information exchanges ( such as 
 partial correlation [ 19 , 72 , 138141 ] ) ; 
 discriminate causality from simple co - occurrence ( such as granger causality [ 138 , 142144 ] ) . 

some methods are able to deal with one aspect of the problem , but none has been 
 proposed to answer all these questions simultaneously . besides , 
 investigation of large - scale networks face a very interesting problem , namely 
 that of determining the spatial precision under which data should be considered 
 as segregated and over which they should be said to be integrated . while it is 
 obvious that neighboring voxels share a great deal of information , methods that 
 model and summarize the behavior of a whole network with one single time course 
 clearly oversimplify the problem and discard a lot of cogent information .
proposed a statistical model 
 that provides a critical distance that separates segregation and integration . 

however , the 
 parameters that characterize the clustering coarseness are set a priori , when 
 they should be determined by the intrinsic properties of the data and allowed 
 to vary across the brain ( e.g. , between subcortical and cortical structures , 
 which have distinct characteristic spatial extents ) .
at least for this reason , it is a 
 crucial step , because network investigation requires multivariate analyses that 
 are computationally very demanding ( the computational burden roughly 
 exponentialy increase with the number of regions ) . in 
 neurocomputing , models investigating issues very similar to that of large - scale 
 networks have already been developed [ 145148 ] . however , most 
 methods developed so far for effective connectivity , such as structural 
 equation modeling ( sem ) [ 149152 ] , dynamical causal modeling 
 ( dcm ) [ 153155 ] , or generative models  including neural mass models [ 145 , 156 ] and large - scale 
 neural models [ 147 , 157159] , have been of little use to the 
 investigation of extended large - scale networks , since their intrinsic 
 complexity prevent them from modeling systems with that many degrees of 
 freedom ( but see , ) .
methods 
 originating from graph and/or network theories might prove more adapted to such 
 problems [ 161163 ] , 
 since they provide global quantification of structures that , besides from being 
 ubiquitous [ 164 , 165 ] , 
 are not unlike some models of brain networks . using such methods , brain 
 networks
have been shown to exhibit small - world [ 70 , 166170 ] and scale - free [ 171 , 172 ] features .
the 
 fact that networks simultaneously exhibit both properties has strong 
 structural [ 104 , 173 ] and 
 functional [ 174 , 175 ] implications .
being able to 
 devise methods that can deal with both individual and group analyses is also an 
 important issue . at the individual level
, it is essential to assess the 
 significance of the different networks [ 80 , 85 , 176 ] . with procedures of increasing 
 complexity , nonparametric resampling procedures , mostly used in the context of 
 the glm so far ,
this has been done by either considering a model for the group   or solving the problem at an 
 individual level and then performing clustering .
validation of such methods have 
 to be developed ; a first step in this direction has been proposed by calhoun et al . .
though 
 computationally tractable on a large - scale network of n units , even for n large , such a 
 method generates n(n1)/2 correlation 
 coefficients ( e.g. , 4950 for as few as 100 voxels / regions ; 19900 for 200 ; 499 500 for 1000 ) . simply representing these on a graph as is commonly done [ 72 , 140 , 181 ] 

procedures that 
 summarize the information have to be proposed ; these can rely on pca / mds [ 71 , 79 , 182 ] ; 
 they could also use other representational techniques [ 183 , 184 ] .
last , but not 
 least , an essential point to validate and better understand the large - scale 
 network approach in fmri is the comparison with results form other imaging 
 modalities or areas of neuroscience , such as electrophysiology [ 3438 ] , electroencephalography ( eeg ) or 
 magnetoencephalography ( meg ) [ 39 , 125 , 185 , 186 ] , and diffusion 
 tensor imaging ( dti ) [ 187190 ] . to be able to efficiently 
 compare results from different imaging modalities , it is essential to better 
 understand how each modality images the activity of large - scale brain networks . 
 in this perspective , providing a unified generative and/or statistical model 
 for several of these modalities would be of the utmost importance , granting 
 access to multimodal in vivo imaging of the brain in action .
 a large - scale brain network can be defined as a set of segregated and integrated 
 regions , that is , distant regions that share strong anatomical connections 
 and functional interactions . 
 data - driven investigation of such networks has 
 recently received a great deal of attention in blood - oxygen - level - dependent 
 ( bold ) functional magnetic resonance imaging ( fmri ) . 
 we here review the 
 rationale for such an investigation , the methods used , the results obtained , 
 and also discuss some issues that have to be faced for an efficient exploration . 
1. INTRODUCTION
2. LARGE-SCALE NETWORKS AS A CONSEQUENCE  OF BRAIN ORGANIZATION

3. fMRI INVESTIGATION OF  LARGE-SCALE NETWORKS

4. TYPOLOGY OF NETWORKS EXTRACTED WITH fMRI
5. FUTURE ISSUES