Supplementary Information to: Topological insights into dense frictional suspension rheology: Third-order loops drive discontinuous shear thickening

In this document, we provide details about (i) average stress contribution per loop order l, (ii) number of loops nl vs l, (iii) contact network evolution with strain, (iv) evolution of loop structure, (v) higher order loop n5-n8, (vi) isolated and connected edges for different µ. These analyses complement the ones presented in the main text.