In standard graph clustering/community detection, one is interested in partitioning the graph into more densely connected subsets of nodes. In contrast, the  search  problem of this paper aims to only find the nodes in a  single  such community, the target, out of the many communities that may exist. To do so , we are given suitable side information about the target; for example, a very small number of nodes from the target are labeled as such. We consider a general yet simple notion of side information: all nodes are assumed to have random weights, with nodes in the target having higher weights on average. Given these weights and the graph, we develop a variant of the method of moments that identifies nodes in the target more reliably, and with lower computation, than generic community detection methods that do not use side information and partition the entire graph.
['Avik Ray', 'Sujay Sanghavi', 'Sanjay Shakkottai']
Searching For A Single Community in a Graph