In my opinion, I think a 4-connected ligand should be represented by 4-c nodes. Using  3-c nodes to represent a 4-connected ligand will result in loss of structural information. Such simplification is not useful in other applications were the knowledge of topology is applied especially in reticular synthesis as suggested by O’Keeffe and Yaghi.

I don't think it's a good idea to change the real connection number for discribing strucuture. Becuse topology simplification is a way to study the nature of the structure, this simplification method have certain rules, if we don't follow the rules, the simplified structure will have no meaning in topology.

What about cases such as this:

If all four carboxylates are connected to form the framework this would be classified as a 4-connected node, so the right hand figure would be most appropriate. Clearly the way you determine network connectivity will have a big effect on the resulting topology, and this is actually key to the whole process. If the ligand in the picture only uses 3 carboxylates to form the network with one remaining free (uncoordinated) then it would be a 3-connected node. You also have to bear in mind that most framework structures will be distorted from the ideal topology.

Hope that's useful.

The example of the ligand given by Lars  was used to assemble MOF 505 which is linked by linked by CU2 paddle wheels. Placing a node at each centre of the phenyl ring and at the centre of the paddle wheel will generate a binodal 3,4 –connected net. If one consider merging the two phenyl rings together, and make it a single node as well as placing another node at the centre of the paddle wheel, then a binodal 4,4- connected net is formed. This net does not resemble the original structure, hence placing the nodes at the centre of the phenyl rings will preserve the structural information. Although topology has to do with structural simplification, its is very important that the structural information is not lost.

What about these two cases then, it is really reasonable to give them different node assignments?

This would be more like the image below than the cross I think, an example of a decorated 4-connected node, essentially replacing a node of N-connectivity (4 in this case) by N-vertices (i.e. the rectangle), a strategy typically employed to increase pore size in network structures (see Yaghi/O'Keeffe). You could describe both in this way since the Ag ion is acting as a link between the 3-connected nodes/ligands if you take this unit as a whole - similar to an SBU if you like. Not sure what the rest of the network looks like connected through the dicarboxylates, but as long as it is clear how you've defined network connectivity then I do not see a problem either way. As an example, HKUST-1 can be described as a 3,4-connected twisted boracite net taking the paddlewheels and BTC linkers as the nodes, but it could equally be described as pcu (as in the original Science paper I think) if one takes a larger unit as the node. Either is valid.

In order to assign nodes there mast be an appropriate reason to do so. First of all topology describes (for the time being) mostly binodal nets but it can find expression in trinodal etc nets in the future. In a mof usually one node is the metal cluster and usually the linkers are the linkages in the topology. When we have a tridentate or more ligand then usually we also see them as nodes. If when studying a topology it is difficult to correlate a topology with anet we have to decorate it, ie chose parts of the net to act as a node. In your case I guess that the chemistry indicates that u use the cross. when applying topological studies on anet you have first to find the different segments. in your case unless there is no other ligand it is the inorganic SBU and the organic linker. You then find the gravitational centers of these to and see the connectivity of the two segments in this case the connectivity is 4 and you cannot change it. In the case of the linker with the Ag ion the metal cation has no other usage on the linker otherthan link the two parts of the linker, ie it is simply a part of the ligand. If you make it two nodes the center is in the bond between the two phenyls and this has no chemical sence. plus you add an extra node and extra lincage .... So if you have no other reason to do it so... ie you cannot find the topology because it is a trinodal net there is no reason to do so. Of cource you can do it if it leads to another binodal net, both would be right. 

Both cases should have the same topology, the Ag ion in the first case acts as a linker between the two ligands. However, if the Ag ion had a connectivity greater than two, then, it would be reasonable to place a node at that metal ion.

This is further discussed here, please comment either here or directly at:

https://www.researchgate.net/publication/282752333_Terminology_Guidelines_and_Database_Issues_for_Topology_Representations_in_MOFs

Research Terminology Guidelines and Database Issues for Topology Repr...