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Mason Alexander Porter wrote:
> The 'modularity is force-directed layout' paper is a relevant one for 
> your question as indicated (and the one that came to my mind as well), 
> but the relation it actually shows between visualization and clustering 
> is between clustering via maximizing modularity and visualization via 
> force-directed layout such as Fruchterman Reingold.  The specific 
> relation you mentioned isn't actually shown in there and spring 
> embedders like Kamada Kawai were not the ones shown to have that 
> relation (though I should also mention that I've definitely seen some 
> potentially relevant similarities in KK as well that it would be nice if 
> somebody quantified...).

It seems to me unlikely that any relation to the Kamada-Kawai algorithm
exists.  The Kamada-Kawai algorithm uses spring constants whose value
depends on the length of the shortest path between a node pair.  And the
shortest path, unfortunately, has no simple mathematical expression in
terms of the graph Laplacians or adjacency matrices upon which clustering
algorithms are based.

The similarity in the group structure found by the Kamada-Kawai algorithm
and standard clustering methods is, probably, just a result of the fact
that any decent clustering method will find approximately the same groups
in a network where the group structure is strong.  (This is almost
tautological, since a clustering method that failed to find strong group
structure present in a network could hardly be called "decent".)


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