Re: [igraph] node diversity (node entropy) versus graph entropy?

[Tamás Nepusz]

I cannot comment on the connection between node entropy and graph entropy as 
defined in Simonyi's paper. However, the concept of edge entropy as you 
describe it can easily be defined in terms of the node entropy (I think). It is 
a common trick to extend a node-related measure to an edge-related one by 
simply taking the line graph of the original graph and then calculating the 
node-related measure on a given node of the line graph, knowing that each node 
of the line graph corresponds to an edge in the original graph. In this sense, 
the edge entropy of edge X in a graph is simply the node entropy of the node 
corresponding to edge X in the line graph, assuming that edge-related 
properties like weights are "transferred" to the line graph as node-related 
properties.

Cheers,
T.

On 28 Oct 2013, at 17:06, David Robinson <address@hidden> wrote:

> I realize that this isn't specifically an igraph question, but it got
> bounced around to/from various Stackexchange forums as not being
> applicable so I'm venturing to pose the question here (while I attempt
> to address the questions about my question to a Stackexchange forum).
> 
> Eagle, et al  discuss the notion of node entropy and this is captured
> in igraph via the diversity metric. In this case, node diversity is a
> (normalized) measure of Shannons entropy for a particular node. I was
> wondering if there was any relationship between these node entropies
> and the idea of the entropy for the entire graph.  There are a few
> definitions of graph entropy, but I am referring to that suggested by
> the infamous Gabor Simonyi in the 2013 DIMACS paper 'Graph Entropy: A
> Survey'.
> 
> A related question: Does the concept of edge entropy make sense? The
> probability would be the ratio of the weight of the edge in question
> and the sum of the weights of all edges connected to the nodes that
> define the edge in question. I realize that this function isn't in
> igraph, but it's an important concept for how I'd like to characterize
> a weighted graph.
> 
> 
> Many thanks in advance,
> David
> 
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