Virtual communities have become an important new organizational form and yet relatively little is known about the conditions which lead to their success. In an attempt to address this knowledge gap, a particular subset of virtual communities - open source software project communities - is investigated and four hypotheses are asserted which relate social network structure to community success. The hypotheses, which are based on social network theory and related research, suggest that success is supported by high levels of affiliation with other communities, moderate levels of density within the network of community conversations, moderate levels of density in the communications between peripheral members and core members, and low levels of density in the communications between administrators and the rest of the community. Empirical research is underway to test these hypotheses based on a sample of over 200 open source software project communities.