K-core analysis of jamming and shear thickening transitions

We analysis the contact network features of packings near the jamming and shear thickening transitions using graph theoretical tools. We find that the 3-core is a precursor of both transitions. This k-core emerges suddenly and discontinuously around a coordination number of 3.35 in agreement with the random graph theory of k-core percolation of Pittel, Spencer and Wormald (1996). This indicates that the k-core is a useful graph feature to understand commonalities between jamming and shear thickening transitions in packings.