Wireless and ad hoc networks often have local regions of highly intra-connected modules or communities of nodes against a backdrop of sparser longer-range inter-community connectivities. We report on empirical observations and a prototype algorithm for correctly counting and labelling the number of dense community structures or modules within a fully connected network. We describe the eigen-spectral method applied to the Laplacian characteristic matrix. We illustrate the effect of different network characteristics on the eigen-spectrum and on properties of the eigenvectors corresponding to the Nc smallest eigenvalues in networks with Nc such dense community modules.
Keywords: wireless networks; ad hoc networks; community structure; modules; eigen-spectra; smallest eigen-values.
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