1. A computer system, comprising: one more processors; and one or more computer-readable media having stored thereon computer-executable instructions that are executable by the one or more processors to insert new nodes into a graph diagram, including performing at least the following: display a graph diagram reflecting a first version of a graph that comprises a plurality of nodes; identify one or more new nodes that are to be added to the graph diagram, based on a second version of the graph that includes the one or more new nodes; create an updated graph diagram reflecting the second version of the graph, while preserving a layout of the plurality of nodes from the graph diagram, including: identifying one of the plurality of nodes as an anchor node in the second version of the graph, the anchor node being either (i) coupled to one of the new nodes, or (ii) coupled to a floating node; creating a disjoint graph diagram, based at least on performing an automatic graph layout of the anchor node and the one or more new nodes; identifying one or more spatial offsets from the anchor node to each of the one or more new nodes in the disjoint graph diagram; and adding the one or more new nodes to the first graph diagram, while maintaining the one or more spatial offsets, resulting in the second graph diagram; and display the second graph diagram.