Nodal domain partition and the number of communities in networks

It is difficult to detect and evaluate the number of communities in complex networks, especially when the situation involves an ambiguous boundary between the inner- and inter-community densities. In this paper, discrete nodal domain theory is used to provide a criterion to determine how many communities a network has and how to partition these communities by means of topological structure and geometric characterization. By capturing the signs of the Laplacian eigenvectors, we separate the network into several reasonable clusters. The method leads to a fast and effective algorithm with application to a variety of real network data sets