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

[David Robinson]

Tamas, Thanks for the idea; I had not thought of taking advantage of
the dual relationship.  I think my only concern might be the existence
of the associated line graph, or the computational time it would take
to generate.  but enough with the negative vibes… Thanks! definitely
going to give it a go.

On Mon, Oct 28, 2013 at 10:20 AM, Tamás Nepusz <address@hidden> wrote:
> 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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