Modular reorganization of brain resting state networks and its independent validation in Alzheimer's disease patients

Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted considerable recent attention. One of the most sensitive detection methods is optimization of the quality function known as "modularity" over the possible divisions of a network, but direct application of this method using, for instance, simulated annealing is computationally costly. Here we show that the modularity can be reformulated in terms of the eigenvectors of a new characteristic matrix for the network, which we call the modularity matrix, and that this reformulation leads to a spectral algorithm for community detection that returns results of better quality than competing methods in noticeably shorter running times. We demonstrate the algorithm with applications to several network data sets.

We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

Recent research on Alzheimer's disease (AD) has shown that cognitive and memory decline in this disease is accompanied by disrupted changes in the coordination of large-scale brain functional networks. However, alterations in coordinated patterns of structural brain networks in AD are still poorly understood. Here, we used cortical thickness measurement from magnetic resonance imaging to investigate large-scale structural brain networks in 92 AD patients and 97 normal controls. Brain networks were constructed by thresholding cortical thickness correlation matrices of 54 regions and analyzed using graph theoretical approaches. Compared with controls, AD patients showed decreased cortical thickness intercorrelations between the bilateral parietal regions and increased intercorrelations in several selective regions involving the lateral temporal and parietal cortex as well as the cingulate and medial frontal cortex regions. Specially, AD patients showed abnormal small-world architecture in the structural cortical networks (increased clustering and shortest paths linking individual regions), implying a less optimal topological organization in AD. Moreover, AD patients were associated with reduced nodal centrality predominantly in the temporal and parietal heteromodal association cortex regions and increased nodal centrality in the occipital cortex regions. Finally, the brain networks of AD were about equally as robust to random failures as those of controls, but more vulnerable against targeted attacks, presumably because of the effects of pathological topological organization. Our findings suggest that the coordinated patterns of cortical morphology are widely altered in AD patients, thus providing structural evidence for disrupted integrity in large-scale brain networks that underlie cognition. This work has implications for our understanding of how functional deficits in patients are associated with their underlying structural (morphological) basis.