Graph addition

[ghost]

Is not being able to come up with a standard definition for adding graphs a burden? One if the other questions mentioned other ways of analyzing graphs, and although we haven't gotten to that lecture yet, is there a good example of when we would really really like to be able to add graphs as opposed other methods?

[mrjiaruiwang]

What does "adding" graph mean biologically? I'm a little confused how that would work. Mathematically, we can add graphs all we want but I don't know if we're necessarily allowed to do it if we are concerned with the biological correctness of the model.

[edunnwe1]

I think that adding a graph biologically might make sense if you are reconciling graphs from different areas or different scales (assuming adding would look like some union of the sets of vertices and edges). Suppose you have a graph of primary visual cortex and someone else has a graph of secondary visual cortex and you want to graph the visual system. Then you might want to 'add' these two graphs so that when you are considering connectivity between areas you also have a view of the edges and nodes already identified in the areas individually, since maybe this informs the connectivity between areas. Or, perhaps you had a working graph of the corticothalamic circuit but then you discovered a 'microcircuit' of interneurons with the thalamic reticular nucleus, and you want to add this to your existing graph of the corticothalamic circuitry. Just guessing, though, I'm not familiar with this literature.

[mblohr]

Perhaps "fusing" rather than "adding" is another way to look at this. If there are two connectomes or, say, atlases, of the brain, how does one fuse these graphs?