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.
D. Kempe, J. Kleinberg, and E. Tardos. KDD '03: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, page 137--146. ACM Press, (2003)