Analysis of how histories of violence are represented and received in cultural institutions such as museums and memorials is frequently framed in terms of conflict and hierarchies or competitions of suffering. In this article the author proposes a framework that imagines the broader and interconnected networks in which museum narratives and ideas about historical violence are represented and debated. The "networked" framework described here provides new ways of understanding how social conflicts such as "competitions of victimhood" play out in multiple and mutually reinforcing arenas.