  Our goal is to quickly find top $k$ lists of nodes with the largest degrees
in large complex networks. If the adjacency list of the network is known (not
often the case in complex networks), a deterministic algorithm to find a node
with the largest degree requires an average complexity of O(n), where $n$ is
the number of nodes in the network. Even this modest complexity can be very
high for large complex networks. We propose to use the random walk based
method. We show theoretically and by numerical experiments that for large
networks the random walk method finds good quality top lists of nodes with high
probability and with computational savings of orders of magnitude. We also
propose stopping criteria for the random walk method which requires very little
knowledge about the structure of the network.
