Nodes = simulated neurons placed on a circle; edges = synapses, wired as an Erdos-Renyi random graph at the chosen density. Every step removes real edges from the live adjacency list, then a real multi-source BFS from every node recomputes exact shortest-path distances over the current graph -- no estimation.
Global efficiency (Latora & Marchiori, 2001):
E = 1/(N(N-1)) * sum_{i != j} 1/d(i,j)
where d(i,j) is the real BFS shortest-path length (unreachable pairs contribute 1/Infinity = 0). This is the standard way to score a disconnected graph, since average path length alone is undefined once components split off.
Random pruning removes a uniformly random surviving edge each step -- a rough model of undirected synaptic attrition. Weakest-first pruning assigns every edge a fixed simulated "usage strength" at creation (drawn once, held constant) and always removes the globally weakest surviving edge -- a model of activity-dependent pruning, where synapses that carry little traffic are eliminated first while frequently-used, well-integrated connections (often hubs' edges) survive longest. Because the strong edges tend to be the ones holding the network's giant component together, weakest-first pruning empirically keeps global efficiency higher for longer than random pruning at the same number of edges removed -- an emergent result of these two rules, not a scripted outcome.