One can gain a lot of insight into the structure of a network by analzing the eigenvalues and eigenvectors of its adjacency matrix. The connection between spectral parameters and the more combinatorial properties of networks and datasets is a subtle issue, and while many results have been established about this connection, it is still not fully understood. This connection has also led to a number of applications, including the development of link analysis algorithms for Web search.
J. Scripps, P. Tan, and A. Esfahanian. Proceedings of the 9th WebKDD and 1st SNA-KDD 2007 Workshop on Web Mining and Social Network Analysis, page 26--35. New York, NY, USA, ACM, (2007)