  Dense granular materials and other particle aggregates transmit stress in a
manner that belies their microstructural disorder. A subset of the particle
contact network is strikingly coherent, wherein contacts are aligned nearly
linearly and transmit large forces. Important material properties are
associated with these force chains, but their origin has remained a puzzle. We
classify subnetworks by their linear connectivity, and show the emergence of a
percolation transition at a critical linearity at which the network is sparse,
coherent, and contains the force chains. The subnetwork at critical linearity
closely reflects the macroscopic stress and explains distinctive features of
granular mechanics.
