An apparatus and method are provided for rapidly ranking network nodes according to input ranking criteria. The links (i.e., first-order paths) between nodes are expressed in a first-order path matrix, which is used to generate nth-order path matrices as nth powers of the first-order path matrix and summed as a power series to generate a surrogate ranking operator (SRO) representing as a single matrix operation a sum over paths of all orders. Thus, in contrast to conventional ranking methods that require multiple recursive steps to account for the interrelatedness of linked nodes, a ranking is produced by multiplying the SRO by a state vector representing the input ranking criteria.