Converted from comment
Most of the time, "network geometry" doesn't make too much sense. You build networks as a bus, in stars, trees, rings but these are topologies. Above the actual topology you might use "architecture" for a more abstract scope.
The links you've given provide very abstract views on networking concepts. I'm not at all sure in how far they are of practical use.
While there are somewhat geometric views in networking including "network diameter", "tree depth", "bisection bandwidth", these views help you handle the complexity of a larger network better, identify potential bottlenecks or breaking points before they happen.
However, when designing a network you don't start with geometric considerations. You start with a proven, best practice topology and adapt that to your current needs.