Exploring recent developments in spectral clustering, we discovered that relaxing a spectral reformulation of Newman's Q-measure (a measure that may guide the search for-and help to evaluate the fit of - community structures in networks) yields a new framework for use in detecting fuzzy communities and identifying so-called unstable nodes. In this note, we present and illustrate this approach, which we expect to further enhance our understanding of the intrinsic structure of networks and of network-based clustering procedures. We applied a variation of the fuzzy k-means algorithm, an instance of our framework, to two social networks. The computational results illustrate its potential.
