of course you can plug the clustering algorithm that you prefer in this phase of spectral clustering. The wide use of k-means embedded in specc is because its simplicity and usually good results.
c-means algorithm is similar to k-means. The difference is that each element has a degree of belonging to clusters (fuzzy theory approach) instead of the deterministic point of view in the membership, when approaching the groups by k-means.
Kavitha, you can use connected component algorithm, Meila and Shi algorithm, Kannan Spectral algorithm instead of K-mean algorithm. You can refer the attached paper for the comparison among the algorithms.
if this question might be still interesting to you, we found that the application of k-means is actually motivated by the minimum cut objective. So in principle, you can use any clustering algorithm but if you want to minimize the ratio/normalized cut then it makes sense to use k-means. We explored this relationship and used our insights to define a more robust version of spectral clustering here:
Conference Paper The SpectACl of Nonconvex Clustering: a Spectral Approach to...