Eagle, et al  discuss the notion of node entropy and this is captured in igraph via the diversity metric. I was wondering if there was any relationship between these node entropies and the idea of the entropy for the entire graph.
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 incident to the edge in question.
: N. Eagle, M. Macy, and R. Claxton, “Network Diversity and Economic Development,” Science, vol. 328, no. 5981, pp. 1029–1031, May 2010.