District heat networks can make a significant contribution to decarbonising domestic heat supply and have been successfully applied in a number of countries. Traditionally, district heat networks have been analysed at the local or city district scale. Performing this analysis at national scale presents new methodological challenges. Efficient techniques are required to work with large datasets and enable rapid iteration of results. As district heating fundamentally involves networks, graph theory is highly relevant for providing well established analysis methods that can scale to very large datasets. Two applications of graph theory are presented for this work. The first presents a method for estimating minimum pipe lengths needed to connect buildings, from which demand densities may be derived. The second presents a graph-based clustering method for connecting distributed supplies and demand regions. These methods have been applied as Swiss national scale.