1. A system configured to utilize an anchor node to efficiently insert one or more additional nodes into a graph diagram visualization while preserving layout of existing nodes in the graph diagram visualization, the system comprising: one or more processors; and one or more computer-readable media having stored thereon computer-executable instructions representing at least a new graph creation tool, a layout tool, and a combiner tool, the computer-executable instructions, when executed at the one or more processors, cause the new graph creation tool to perform at least the following: receive a second version of a graph, which comprises: one or more existing nodes already existing in a first graph diagram visualization that reflects a first version of the graph, and one or more new nodes to be added to the first graph diagram visualization as part of creating a second graph diagram visualization that reflects the second version of the graph; identify, in the second version of the graph, the one or more new nodes to be added to the first graph diagram visualization; identify, in the second version of the graph, one or more anchor candidate nodes, from among the one or more existing nodes, that are each coupled to at least one of the one or more new nodes in the second version of the graph, wherein each anchor candidate node is coupled directly, with no intervening node, to at least one of the one or more new nodes in the second version of the graph; and create a new graph from the one or more new nodes to be added to the first graph diagram visualization and from the one or more anchor candidate node, the new graph excluding any of the one or more existing nodes that is not directly coupled to at least one of the one or more new nodes; the computer-executable instructions, when executed at the one or more processors, further cause the layout tool to automatically create a disjoint graph diagram from the new graph based at least on the new graph creation tool having created the new graph; and the computer-executable instructions, when executed at the one or more processors, further cause the combiner tool to automatically create the second graph diagram visualization, by performing at least the following: select one of the one or more anchor candidate nodes as an anchor node; identify a spatial offset from the anchor node to each of the one or more new nodes that is coupled to the anchor node in the disjoint graph diagram; add each of the one or more new nodes to the first graph diagram visualization to create the second graph diagram visualization, which includes the one or more new nodes, while maintaining the identified spatial offset for the one or more new nodes to the anchor node in the second graph diagram visualization; and convey the second graph diagram visualization for display at a display device.