CS599: Structure and Dynamics of Networked Information (Spring 2005) 02/07/2005: The Search for Communities

We previously looked at communities as simply dense subgraphs graphs, or as subgraphs such that each node has a large fraction of its edges inside. Another view, taken in [3], starts from the hubs and authorities model. It argues that a structure of densely linked hubs and authorities is a common feature of communities. Such a core, a dense bipartite graph, can be considered the “signature” of a community Ideally, we would like to enumerate all such signatures, and expand them to communities. However, the complexity of doing so would be prohibitive. In fact, even finding just one large complete bipartite graph is NP-hard. However, when the given graph is dense enough, it always has a large complete bipartite subgraph.