I study the Web using spectral methods. This includes studying individual networks such as Facebook, Twitter, Wikipedia, etc., as well as the Web as a whole in the form of semantic networks. My PhD thesis is about the spectral analysis of individual networks; my post-doctoral work will expand to semantic networks.

My work can be applied on three levels:

• Network characteristics: Connectedness, balance, conflict, clustering, etc.
• Node characteristics: Trust, popularity, centrality, etc.
• Link analysis: link prediction, rating prediction, recommendation, personalized ranking, etc.

The methods I use are spectral, i.e. they are based on characteristic graph matrices such as the adjacency matrix and the Laplacian matrix. I am particularly interested in ways to formulate network mining algorithms algebraically to find connections to other algorithms. In fact, my view is that all link prediction algorithms can be expressed over all paths between two nodes in the network, given suitable operations for aggregating adjacent and parallel edges. These two operations can be reduced to multiplication and addition in a suitable semiring, where link prediction functions can be expressed as a function of the corresponding adjacency matrix. This justifies algebraic graph theory. If additionally the operations form a field, spectral analysis can be used to simplify the computation of link prediction functions, because most of them can be seen as spectral transformations of the adjacency matrix.

To apply spectral methods to the Semantic Web, I am looking for ways to extend algebraic graph theory to arbitrary edge labels. A first step in this direction is to analyse networks with negatively weighted edges, of which the Slashdot Zoo is a prime example. In this case, the real adjacency matrix can be used, and spectral analysis is possible.