Leadership Insularity: A New Measure of Connectivity Between Central Nodes in Networks.

We combine two foci of interest with respect to community identification and node centrality and create a novel metric termed "leadership insularity." By determining the most highly connected nodes within each community of a network, we designate the 'community leaders' within the graph. In doing this, we have the basis for a novel metric that examines how connected, or disconnected, the leaders are to each other. This measure has a number of appealing measurement properties and provides a new way of understanding how network structure can affect its dynamics, especially information flow. We explore leadership insularity in a variety of networks.