On preferred states of agents: how global structure is reflected in local structure

We investigate the correlation between the information theoretic measure of empowerment and the graph theoretic measure of closeness centrality, to better understand the structural conditions that must exist in a world for learning and adaptation. We examine both measures in both a simple gridworld scenario, represented as a graph, and on a scale-free graph. We show a strong correlation between the two measures, and discuss the strengths and weaknesses of both. We go on to show how the local measurement of empowerment can in many cases predict a measure for the global measurement of closeness centrality.