Bugs are inevitable in software projects. Resolving bugs is the primary activity in software maintenance. Developers, who fix bugs through code changes, are naturally important participants in bug resolution. However, there are other participants in these projects who do not perform any code commits. They can be reporters reporting bugs; people having a deep technical know-how of the software and providing valuable insights on how to solve the bug; bug-tossers who re-assign the bugs to the right set of developers. Even though all of them act on the bugs by tossing and commenting, not all of them may be crucial for bug resolution. In this paper, we formally define essential non-committers and try to identify these bug resolution catalysts. We empirically study 98304 bug reports across 11 open source and 5 commercial software projects for validating the existence of such catalysts. We propose a network analysis based approach to construct a Minimal Essential Graph that identifies such people in a project. Finally, we suggest ways of leveraging this information for bug triaging and bug report summarization.