Maybe I can clear up the confusion: "Show entire graph" does not necessarily put (0,0) in the center, but the center of the bounds of the whole graph. If there is only one node in your diagram, this node will end up in the center of the viewport. However, if there are several elements in the graph, the center of the viewport will be the center of the bounds of the entire graph. E.g. suppose there are two nodes, one with x=200, y=100, width=30, height=30 and one with x=400, y=500, width=80, height=60, then the bounds of the entire graph will be x=200, y=100, width=280, height=460. In this case, x=340, y=330 will end up being the center of the viewport after the "Show entire graph" operation.
If there are no elements, it is kind of debatable what constitutes the center of the whole graph. From a implementation point of view, it does make sense to assume width=0 and height=0 for the bounds of a graph with no elements. In this case, "Show entire graph" will center on the x and y coordinates of the graph bounds. Since there are no elements, there is not really a right or wrong choice for x and y. We did choose x=0 and y=0 because 0 is the default value for numbers in Java (the programming language that was used to create yEd). As a result, "Show entire graph" centers on (0,0) if there are no elements. Again, from an implementation point of view this make sense, because this means that there are no special cases for "Show entire graph".
By the way, negative coordinates do not become available only after "Show entire graph" - they are available right from the start.
E.g. start with an empty document. Create one node. Select said node. Now specify negative coordinates for the node's x and y properties in the properties view in yEd's lower right corner. If you specify small enough values, this will actually "move" the selected node out of the current viewport. "Show entire graph" will again center the viewport on the node resulting in the viewport center having negative coordinates.