Nodes in this form are enumerated unambiguously.
Each of names consists of circle's number and node's number in its circle.
The nodes are connected horizontally, vertically, diagonally, and 'circularly', as shown on image above.
Perhaps we should also enumerate connections unambiguously, or intersections. Or we can use 'automatic' names for each of the intersections, being constructed from all node names adjacient to a given intersection.
Information in this form can travel in 1-3 hops from any source to any destination.
There are many ways for information to travel, so it can be considered secure, and robust (resistant to failures).
There are no 'central point' that is part of shortest path to (almost) every node, thus effectively a traffic bottleneck.
Perhaps cost of connection links is high, but that's one of approaches... security, robustness and speed comes at cost.
It can be easily extended by adding nodes at (not neccessarily all) intersections (but not only there it makes sense), but that changes its qualities somehow.
See also: Shapes & Forms.