The data used in this work were part of the 1,000 Functional Connectomes Project (http://fcon_1000.projects.nitrc.org/
), a collection of resting-state fMRI data sets from a number of laboratories around the world. Of all the data sets available, 4 data sets from 4 different sites (Baltimore, Leipzig, Oulu, and St. Louis), consisting of n
194 subjects in total, were selected because (i) these data sets consisted of young to middle-aged subjects (20–42 years old) and (ii) these data sets were acquired while subjects’ eyes were open and fixated on a cross. The original resting-state fMRI data were processed using the same preprocessing pipeline available in our laboratory (see Materials and Methods
). Networks were formed by calculating a correlation coefficient for every voxel pair then by thresholding the resulting correlation matrix to identify strong correlations. The threshold was adjusted for each subject in a way that the density of connections was comparable across subjects (see Materials and Methods
). Each voxel was treated as a node in the resulting network. Each subject’s network consisted of an average of 20,743 nodes. Modules in each subject’s network were identified by the Qcut algorithm 
. The algorithm identified sets of nodes that were highly interconnected among themselves and designated them as distinct modules. Each node in the network can only be part of one module at a time.
After modules were identified in all the subjects, the consistency of modules across subjects was assessed using SI. In brief, SI summarizes the overlap of nodes in modules across different subjects while penalizing any disjunction between modules (see Materials and Methods
). SI is calculated at each node, forming an SI image summarizing across-subject consistency of the modular structure. More specifically, each SI value measures how consistently a particular node falls into a particular module. A high SI value indicates that the voxel is located in the same module across subjects, while a low SI value signifies that the voxel is likely part of different modules in different subjects. Theoretically, SI ranges from 0 to n–1 (n–1
193 in this study) 
. However, in practice the SI values are considerably lower than the possible maximum value of n–1 due to disjunction between modules across subjects. shows the SI image generated from all the subjects’ modular organization, thresholded at SI>15. This threshold was maintained throughout the manuscript to facilitate comparison between modular organizations. The areas of high SI correspond to areas that were consistently part of the same modules across subjects. These areas include the occipital lobe, precuneus, posterior cingulate cortex, pre- and post-central gyri, medial frontal gyri and the components of basal ganglia.
Consistency of whole-brain functional modular organization across subjects.
During the calculation of the global SI map shown in , we were able to determine which subject’s module was the most representative at a particular node (see Materials and Methods
. This representative module resulted in the largest SI value at that particular voxel location among all the subjects’ modules. To further examine high SI areas, the most representative modules that correspond to the brain regions in were identified. These representative modules were then used to summarize consistency among subjects and SI was calculated with respect to these modules. The resulting images are module-specific SI images and summarize group consistency at a voxel-level. Module-specific SI images are analogous to coefficient of variation (CV) images, which are used in ICA analyses to summarize consistency of RSNs at the voxel-level 
The visual module covers the entire span of visual cortex and includes both primary and secondary cortices (). This module is comparable to ICA components like components A and E in Damoiseaux et al. 
, RSN1 in De Luca et al. 
, and module M2b in Doucet et al. 
. The corresponding module has also been reported in previous functional brain network analyses, including Module II of He et al. 
, Module 4 of Rubinov and Sporns 
, and the posterior module of Meunier et al. 
. Thus, this module is highly consistent among individuals and easily identifiable by both ICA and network methodologies. Moreover, the secondary cortices of the occipital lobe exhibited high SI values (), which is comparable to the reduced variability observed in visual components found by a previous ICA study 
Module-specific SI of four most consistent modules across subjects.
The sensory/motor module () is analogous to the motor network identified by the seed-based correlation method 
. The most consistent regions within this module include the pre- and post-central gyri. On the other hand, the supplementary somatosensory area (S2), surrounding auditory cortex and portions of the posterior insula show reduced consistency across subjects. This module roughly corresponds to component F in Damoiseaux et al. 
, RSN3 in De Luca et al. 
, and module M2a in Doucet et al. 
. Similar to the results reported by Damoiseaux et al. 
, the consistency of this module was lower than that observed for both default mode network (DMN) and visual modules (). Module I of He et al. 
and Module 1 of Rubinov and Sporns 
demonstrate similarities with our sensory/motor module. Interestingly, these previously reported modules also include portions of the insula and auditory cortices. These findings are not only consistent with ours but also to previous reports of the ICA results.
The basal ganglia module () consisted of the caudate, globus pallidus, putamen, and thalamus. It also extended into the medial temporal lobe, temporal pole, parahippocampal gyrus, hippocampus, amygdala and cerebellum. Interestingly, these brain regions have not been consistently classified into one component by ICA. While De Luca et al.’s RSN3 suggests some involvement of the hippocampus and thalamus 
within the motor component, some ICA studies did not find a component similar to this module 
. However, another ICA study by Damoiseaux et al. revealed a component consisting of the thalamus, putamen and insula (component K) 
which led to other ICA studies on connectivity. In particular, the basal ganglia component has been shown to include portions of the striatum, such as the caudate and the globus pallidus 
. Similarly, basal ganglia modules have been previously reported in studies that have used network methodologies. For example, Module V found by He et al. 
and Module 3 by Rubinov and Sporns 
contain all the regions of the basal ganglia. Variations of this have also been described in the central module of Meunier et al. 
and in the RSN3 of De Luca et al. 
. Though these findings contain similar regions as our module, they extend further into the insular and motor cortices. Functional connectivity of the cerebellum with the rest of the basal ganglia proved unique in our results compared to previous network module findings. Although global SI () values did not indicate high modular consistency of the cerebellum across subjects, the module-specific SI map shows that it is consistently part of the basal ganglia module across subjects ().
The default mode network (DMN) 
was also identified as a consistent module across subjects (). This module included the precuneus (PCun), posterior cingulate cortex (PCC), inferior parietal cortex, superior medial frontal cortex, and anterior cingulate cortex (ACC). The PCC exhibited elevated SI values and was found to be the most consistent brain region of the DMN. In comparison, the SI values of the medial frontal gyri were attenuated, indicating this region to be less consistently found in the DMN module.
The intra-modular consistency of this module appeared comparable to the reduced variability of the DMN component found by an ICA 
. While this module covers the brain areas typically considered as part of the DMN, weaker SI in the frontal portion also suggests that the anterior and posterior portion of the DMN may not be as strongly coupled as the rest of the DMN. This may be because the connectivity pattern is slightly different between the anterior and the posterior portions of the DMN. Research supporting this hypothesis includes that of Andrews-Hanna et al. 
using temporal correlation analysis. They determined that the DMN was composed of multiple components, including a medial core and a medial temporal lobe subsystem. Using ICA, Damoiseaux et al. 
described two RSN components that together included the superior and middle frontal gyrus, posterior cingulate, middle temporal gyrus and superior parietal cortices. Finally, the work of Greicius et al. notes some differences in the seed-based connectivity of the DMN when the seed was placed in either the PCC or the ventral ACC 
Among the modules shown in , there were more than one choice for the most representative subject in the sensory/motor module and the default mode module. This can be seen in showing the image of the most representative subject by voxel locations. Within the motor / sensory strip and the precuneus, there were two subjects with the highest SI values. Even though either of these subjects could serve as the representative subject for these modules, the overall consistency of the entire module was still captured, as the module specific SI images appear strikingly similar even if different subjects were chosen as the representative subject ().
Multiple representative individuals produce similar module-specific SI maps.
The number of modules in seems surprisingly few, especially when compared to previous reports of ICA 
. Our results, however, do not indicate the absence of modules similar to previously found ICA components. Instead, some were only found to be less consistently organized across subjects (). These modules do not necessarily include similar sets of nodes across subjects, and consequently do not exhibit high global SI values (). Two of such modules are the ventral (superior parietal cortex as well as superior and medial frontal gyri) and dorsal (superior parietal cortex, superior and dorsal lateral frontal, and precentral gyri) attention networks identified by previous fMRI analyses 
. A previous ICA finding has combined these two systems into the same component 
while others have separated them into separate components for the left and right hemispheres 
. Here we present two distinct modules corresponding to the separate ventral and dorsal attention systems which have also been found in previous network analyses 
. It is interesting to note that low SI values in our ventral and dorsal attention modules () are in contrast to the stability of corresponding components found using ICA 
Module-specific SI images of modules with limited consistency.
In addition to the ventral and dorsal attention modules, we present a module containing the cerebellum (). Though the cerebellum was found to be consistently connected to the basal ganglia (), many nodes within the cerebellum formed a unique module by themselves. However, reduced module-specific SI values indicate that this module demonstrates limited consistency across subjects. Thus, while the cerebellum may belong to the same module as the basal ganglia in some subjects, in another group of individuals the cerebellum belong to an isolated module as shown in .
We used SI to assess the consistency of modules across subjects rather than calculating the average network, which has been used by some researchers to generate a “summary” network for a study population 
. An average network, which is produced by averaging correlation matrices across subjects, does not properly represent the characteristics of the individual networks 
. Rather, it produces a network whose key modular structure is altered from that of the individual networks. shows an example of such an alteration. In particular, we generated an average network by averaging the correlation matrices from all the subjects (n
194). This average correlation matrix was then thresholded (see Materials and Methods
) and modular organization was then detected on the resulting adjacency matrix. The modular organization of this average network is shown in , with each color denoting a network module. The data used in our analysis represent a subset of the subjects used by Zuo et al. 
and show that modular organization is very similar to theirs. Most striking, however, is the modules associated with the DMN. Using an average network, we found that two distinct anterior () and posterior () modules exist. This is in stark contrast to the DMN module-specific SI image, which does not separate into anterior and posterior parts (). To add further confidence in this finding, DMN modules of the individuals of each data set were examined. We found that the anterior and posterior portions of the DMN were indeed commonly found as one module ().
The modular structure of the average network.
A comparison between the other three SI modules shown in and the two shown in with those from the average network are presented in . Here we show the modules for the visual and motor/sensory cortices as well as the basal ganglia from the average network. These three modules comprise similar areas represented in the module specific SI images of the corresponding modules in . In addition to previously mentioned differences (), we show that average modules corresponding to the ventral and dorsal attention brain regions are quite different than those found using module specific SI in . For instance, averaging correlation matrices across individual subjects resulted in the separation of the left from the right dorsal lateral prefrontal cortex. Neither of these modules included the superior portions of the parietal lobules. Instead, these brain areas were identified as a separate module. Interestingly, this module included bilateral secondary sensory cortices.
Selected modules from the average network.
Averaging alters not only modular organization, but also other network characteristics 
. shows the distributions of node degree, or the number of edges per node, for all n
194 subjects (blue) as well as that of the average network (red). As it can be seen in , the average network has far more low degree nodes than any of the subjects in the data set. However, the average network lacks medium degree nodes and thus its degree distribution drops faster than that of the other individual networks. Various network metrics are also altered in the average network. For example, the clustering coefficient and the path length, describing tight local interconnections and efficient global communication respectively 
, are significantly different (p<0.0001, one-sample T-test) from that of the individual networks (see ). Taking all these observations together, we can conclude that the average network does not accurately represent characteristics of individual networks in the data.
Degree distributions of the average network and individual networks.
Comparison of network characteristics between the average network and individual networks.