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