  Graph centrality measures use the structure of a network to quantify central
or "important" nodes, with applications in web search, social media analysis,
and graphical data mining generally. Traditional centrality measures such as
the well known PageRank interpret a directed edge as a vote in favor of the
importance of the linked node. We study the case where nodes may belong to
diverse communities or interests and investigate centrality measures that can
identify nodes that are simultaneously important to many such diverse
communities. We propose a family of diverse centrality measures formed as fixed
point solutions to a generalized nonlinear eigenvalue problem. Our measure can
be efficiently computed on large graphs by iterated best response and we study
its normative properties on both random graph models and real-world data. We
find that we are consistently and efficiently able to identify the most
important diverse nodes of a graph, that is, those that are simultaneously
central to multiple communities.
