We use lubricated-flow discrete-element-method (LF–DEM) simulations to examine how contact-network organization shapes particle motion in dense shear-thickening suspensions. The primary system studied is a two-dimensional bidisperse monolayer where rigid clusters are identified by the $(3,3)$ pebble game; three-dimensional simulations are shown to have qualitatively similar rotational velocity statistics. Across the stress–solid-fraction state diagram, frictional contact number, $k\ge 3$ percolation, and rigid-cluster fluctuations all strengthen in the same region where translational velocity correlations grow, consistent with coherent translation within rigid clusters and a state-dependent contrast in relative motion between particles inside and outside them. Rotational motion provides a complementary view: non-affine angular-velocity distributions broaden, near-contact non-affine rotational fluctuations become increasingly anti-correlated, and particles inside and outside rigid clusters carry distinct statistics. Connectivity, rigidity, and velocity correlations are related but distinct signatures of the constrained collective motion that accompanies shear thickening and the approach to shear jamming.