  A random walk is known as a random process which describes a path including a
succession of random steps in the mathematical space. It has increasingly been
popular in various disciplines such as mathematics and computer science.
Furthermore, in quantum mechanics, quantum walks can be regarded as quantum
analogues of classical random walks. Classical random walks and quantum walks
can be used to calculate the proximity between nodes and extract the topology
in the network. Various random walk related models can be applied in different
fields, which is of great significance to downstream tasks such as link
prediction, recommendation, computer vision, semi-supervised learning, and
network embedding. In this paper, we aim to provide a comprehensive review of
classical random walks and quantum walks. We first review the knowledge of
classical random walks and quantum walks, including basic concepts and some
typical algorithms. We also compare the algorithms based on quantum walks and
classical random walks from the perspective of time complexity. Then we
introduce their applications in the field of computer science. Finally we
discuss the open issues from the perspectives of efficiency, main-memory
volume, and computing time of existing algorithms. This study aims to
contribute to this growing area of research by exploring random walks and
quantum walks together.
