The United Nations' ambitions to combat climate change and prosper human development are manifested in the Paris Agreement and the Sustainable Development Goals (SDGs), respectively. These are inherently inter-linked as progress towards some of these objectives may accelerate or hinder progress towards others. We investigate how these two agendas influence each other by defining networks of 18 nodes, consisting of the 17 SDGs and climate change, for various groupings of countries. We compute a non-linear measure of conditional dependence, the partial distance correlation, given any subset of the remaining 16 variables. These correlations are treated as weights on edges, and weighted eigenvector centralities are calculated to determine the most important nodes. We find that SDG 6, clean water and sanitation, and SDG 4, quality education, are most central across nearly all groupings of countries. In developing regions, SDG 17, partnerships for the goals, is strongly connected to the progress of other objectives in the two agendas whilst, somewhat surprisingly, SDG 8, decent work and economic growth, is not as important in terms of eigenvector centrality.