The provenance of this question is from page 152 of Entropy - God's Dice Game by Kafri: “How can links be optimally distributed between nodes?” For a static network, energy efficiency might be optimized by scaling the network by its mean path length. Embedded wireless sensors might not operate in a static environment; the material in which they are embedded may alter in its configuration. Cellular phone transmission might not be static, at least as to the cell phones.
A February 2015 article, A Survey on Optimal Nodes Topology in Wireless Sensor Network by Priyanka Tadas and Purnima Soni (International Journal of Computer Science and Network) discusses various possible ways for distributing nodes. Are there other sources of information for this question? Do you have suggestions of your own?
Optimality has to be defined for an objective. What is your objective?
Let me give an example: the global telephone networks. If your objective is to support the possibility of the presidents of two countries A and B to call each other, you just need one link from node A to node B. That's optimal for this case.
Does this help?
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