If I'm reading this question correctly, plotting this universe structure onto a map is a simple matter of plotting points onto 3D space normally, and then adding a 4th dimensional point to each of those points for the portals.
Points are normally plotted (x,y,z), where x, y and z are the 3D planes of existence.
In your universe, you simply have each point labeled (x, y, z, d), where d represents the point in the other dimension. How does this help plot the portal locations though? Well, since the portal locations are stated to be "temporarily the same", the point (x1, y1, z1, d1) would be a different point in the physical universe than the point (x2, y2, z2, d1), but the same point in the alternate dimension - the d1 point. So someone standing at (15, 1, 3, 1) could theoretically open up a portal to a point (3233, 23231, 545, 1), assuming you wanted those 2 points in the universe to have a connection.
Imagine that this picture is one of your maps, perhaps a map of a quadrant of space. In the center of this map is the "origin" of your map, so perhaps a star or something. Note that the x y z coordinates are relative to the origin of the map, (numbers not to scale in this picture) but the 4th number (the "d" number) comes in pairs. This can be used to signify how the different points connect to eachother. So in this map, a person standing on either of the white points can "move" through the portal to get to the other point", and red to red, blue to blue, etc.
In my picture, I used color to differentiate the points because it makes it a bit easier to understand, but of course, you could use only color to differentiate between portals; but then you'd quickly run out of colors that you can discern from the visible eye. This method allows you to link an infinite number of points in the universe together simply by using the same "d" number on the points.