In recent years, there is an increased interest in the role of static properties of and dynamics on signed graphs in physical, biological, and social networks. In particular, community structures of signed graphs and their modularity indices have drawn special attention, and there are numerous methods to identify them. Here we provide the technical details of implementing four important methods that in their nature are very different from one another; two spectral methods , one using the adjacency matrix and one using the Laplacian matrix, a heuristic graph theoretic method using a concept of edge centrality, and finally, a stochastic combinatorial optimization method. Because of the novel nature of the methods , we focus on an interesting problem of community structures in brain network of the CA1 region of the hippocampus of anesthetized rats to study the pre-ictal and post-ictal states. We use recent electroenecephalograph (EEG) depth recordings for a period of 117 minutes at a sampling rate of 1000Hz. Since the electrode used has 16-contact points, we construct non-overlapping but sliding 100 , 000 sample-windowed correlation matricesor functional connectivity (FC) matrices over the recorded time, yielding signed graphs. Our results from the clustering methods both at the pre-ictal and post-ictal periods of the depth recording reported here for the first time yield convincing answers to differing community structures .
Detecting and evaluating regions of brain under various circumstances is one of the most interesting topics in computational neuroscience. However, the majority of the studies on detecting communities of a functional connectivity network of the brain is done on networks obtained from coherency attributes, and not from correlation. This lack of studies, in part, is due to the fact that many common methods for clustering graphs require the nodes of the network to be `positively' linked together, a property that is guaranteed by a coherency matrix, by definition. However, correlation matrices reveal more information regarding how each pair of nodes are linked together. In this study, for the first time we simultaneously examine four inherently different network clustering methods (spectral, heuristic, and optimization methods) applied to the functional connectivity networks of the CA1 region of the hippocampus of an anaesthetized rat during pre-ictal and post-ictal states. The networks are obtained from correlation matrices , and its results are compared with the ones obtained by applying the same methods to coherency matrices. The correlation matrices show a much finer community structure compared to the coherency matrices. Furthermore, we examine the potential smoothing effect of choosing various window sizes for computing the correlation/coherency matrices .
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In recent years, there is an increased interest in
Detecting and evaluating regions of brain under various circumstances is one of the most interesting topics in computational neuroscience. However, the majority of the studies on detecting communities of a functional connectivity network of the brain is done on networks obtained from coherency attributes, and not from correlation. This lack of studies, in part, is due to
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role of static properties of and dynamics on signed graphs in physical, biological, and social networks. In particular, community structures of signed graphs and their modularity indices have drawn special attention, and there are numerous methods to identify them. Here we provide the technical details of implementing four important methods that in their nature are very different from one another; two spectral methods , one using the adjacency matrix and one using the Laplacian matrix, a heuristic graph theoretic method using a concept of edge centrality, and finally, a stochastic combinatorial optimization method. Because of
fact that many common methods for clustering graphs require the nodes of the network to be `positively' linked together, a property that is guaranteed by a coherency matrix, by definition. However, correlation matrices reveal more information regarding how each pair of nodes are linked together. In this study, for the first time we simultaneously examine four inherently different network clustering methods (spectral, heuristic, and optimization methods) applied to the functional connectivity networks of
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novel nature of the methods , we focus on an interesting problem of community structures in brain network of the
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anesthetized rats to study the
an anaesthetized rat during
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We use recent electroenecephalograph (EEG) depth recordings for a period of 117 minutes at a sampling rate of 1000Hz. Since the electrode used has 16-contact points, we construct non-overlapping but sliding 100
The networks are obtained from correlation matrices
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000 sample-windowed correlation matricesor functional connectivity (FC) matrices over the recorded time, yielding signed graphs. Our results from the clustering methods both at the pre-ictal and post-ictal periods of the depth recording reported here for the first time yield convincing answers to differing community structures
and its results are compared with the ones obtained by applying the same methods to coherency matrices. The correlation matrices show a much finer community structure compared to the coherency matrices. Furthermore, we examine the potential smoothing effect of choosing various window sizes for computing the correlation/coherency matrices