Does the Mask Know Where to Cut? Separating Topology from Weight Placement in Rewiring Nulls

Rewiring null models are widely used to test whether the pattern of connections in a weighted network matters. Yet rewiring changes both the connections and the weights assigned to them, so the resulting score combines topology with weight placement. We show that this score decomposes into wiring and placement terms, provide an exact finite-sample test for placement, and separate placement variance from rewiring variance. The construction applies the null’s weight rule to the original topology as well as to rewired topologies, allowing wiring to be compared under the same treatment of weights. In neural-network pruning, placement is significant in all 36 high-sparsity iterative-magnitude-pruning comparisons across three initializations. In connectome reservoirs, it accounts for up to 99.8% of the null variance; removing it from the score difference reduces the statistic’s magnitude, whereas removing its contribution to the variance increases it. A conventional rewiring score is therefore not a biased topology score but a different quantity that combines wiring and weight placement.