Thanks, but the node I want to move is shared between three polygons, and so ArcMap looks at them as different nodes and edges. So, your suggestion works this node:
But not this node, associated with one topology edge...
or for the same node, but associated with a different topology edge...
or for the same node here, but associated with another topology edge:
I can move that node, and the topology edges associated with all three of those edges will move accordingly, but I only want to move the edges up to the next vertex in the polygon to move, not the entire shape of the topology edge as shown when clicking using the topology edit tool. Right now, I can do this:
Which is no bueno. I don't want the other vertices of the polygons - the one's I'm NOT selecting - to move. Hope that's clear, and thanks for the help.