This document summarizes a study on clustering probabilistic graphs. It establishes an edit-distance-based definition of clustering for probabilistic graphs and connects this objective function to correlation clustering. This allows for practical approximation algorithms to be proposed. The methods can discover the correct number of clusters in a protein-protein interaction network and identify established protein relationships, demonstrating their effectiveness. The techniques also proved practical on a large social network with one billion edges.

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CLUSTERING LARGE PROBABILISTIC GRAPHS
ABSTRACT:
We study the problem of clustering probabilistic graphs. Similar to the problem of clustering
standard graphs, probabilistic graph clustering has numerous applications, such as finding
complexes in probabilistic protein-protein interaction (PPI) networks and discovering groups of
users in affiliation networks.
We extend the edit-distance-based definition of graph clustering to probabilistic graphs. We
establish a connection between our objective function and correlation clustering to propose
practical approximation algorithms for our problem. A benefit of our approach is that our
objective function is parameter-free. Therefore, the number of clusters is part of the output.
We develop methods for testing the statistical significance of the output clustering and study the
case of noisy clusterings. Using a real protein-protein interaction network and ground-truth data,
we show that our methods discover the correct number of clusters and identify established
protein relationships. Finally, we show the practicality of our techniques using a large social
network of Yahoo! users consisting of one billion edges.