We provide a proximal average with repect to $1$-coercive Legendre function. In the sense of Bregman distance, envelope is convex combination envelopes individual functions. The mapping convexified mappings Techniques from variational analysis keys for average.

Connectivity and edge-connectivity of a graph measure the difficulty of breaking the graph apart, but they are very much affected by local aspects like vertex degree. Average connectivity (and analogously, average edge-connectivity) has been introduced to give a more refined measure of the global “amount” of connectivity. In this paper, we prove a relationship between the average connectivity a...