From clusters to queries: exploiting uncertainty in the modularity landscape of complex networks.

Uncovering latent community structure in complex networks is a field that has received an enormous amount of attention. Unfortunately, whilst potentially very powerful, unsupervised methods for uncovering labels based on topology alone has been shown to suffer from several difficulties. For example, the search space for many module extraction approaches, such as the modularity maximisation algorithm, appears to be extremely glassy, with many high valued solutions that lack any real similarity to one another. However, in this paper we argue that this is not a flaw with the modularity maximisation algorithm but, rather, information that can be used to aid the context specific classification of functional relationships between vertices. Formally, we present an approach for generating a high value modularity consensus space for a network, based on the ensemble space of locally optimal modular partitions. We then use this approach to uncover latent relationships, given small query sets. The methods developed in this paper are applied to biological and social datasets with ground-truth label data, using a small number of examples used as seed sets to uncover relationships. When tested on both real and synthetic datasets our method is shown to achieve high levels of classification accuracy in a context specific manner, with results comparable to random walk with restart methods.