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If relationships and connectivity are the focus of interest -- as they are
with infectious diseases -- then the line graph is a great way to
summarize this.  We've used the mean degree of the line graph to represent
the epidemic potential in a network.  For intuition, note that the rule of
serial monogamy produces isolated dyads, and the resulting line graph has
no links. The higher the mean degree, the more connected and centralized
the network.

mm

On Thu, 18 Sep 2003, Ulrik Brandes wrote:

> *****  To join INSNA, visit http://www.sfu.ca/~insna/  *****
>
> On Thu, Sep 18, 2003 at 10:32:00AM +0900, ?? ???? wrote:
> > But, what's the meaning to make line to node? Can we have meaningful
> > anaylsis result?
>
> Among other things, they are a useful tool for defining structural importance
> of edges:  just apply a node centrality measure on the line graph.
>
> Note, however, that these do not necessarily agree with other straightforward
> generalizations (e.g., it can be proven that no reasonable node centrality on
> the line graph gives the same ranking as edge betweenness).
>
> B.
>
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