  We study a family of random graph models - termed subgraph generated models
(SUGMs) - initially developed by Chandrasekhar and Jackson in which
higher-order structures are explicitly included in the network formation
process. We use matrix concentration inequalities to show convergence of the
adjacency matrix of networks realized from such SUGMs to the expected adjacency
matrix as a function of the network size. We apply this result to study
concentration of centrality measures (such as degree, eigenvector, and Katz
centrality) in sampled networks to the corresponding centralities in the
expected network, thus proving that node importance can be predicted from
knowledge of the random graph model without the need of exact network data.
