off topic: Regarding Figure 8: "a graph with 10 nodes, each having 4 neighbors and no two shards requiring more than 2 hops for cross-shard communication". This

off topic: Regarding Figure 8: "a graph with 10 nodes, each having 4 neighbors and no two shards requiring more than 2 hops for cross-shard communication". This can be achieved with only 3 neighbors (Petersen graph) https://en.wikipedia.org/wiki/Petersen_graph https://en.wikipedia.org/wiki/Petersen_graph More about this here: https://en.wikipedia.org/wiki/Table_of_the_largest_known_graphs_of_a_given_diameter_and_maximal_degree https://en.wikipedia.org/wiki/Table_of_the_largest_known_gra...