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

[David Robinson]

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