Before revision: 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.
After revision: In recent years, there is an increased interest in 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 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.