  Graph sampling is a technique to pick a subset of vertices and/ or edges from
original graph. Among various graph sampling approaches, Traversal Based
Sampling (TBS) are widely used due to low cost and feasibility for many cases,
in which Simple Random Walk (SRW) and its variants share a large proportion in
TBS. We illustrate the foundation SRW and presents the problems of SRW. Based
on the problems, we provide a taxonomy of different Random Walk (RW) based
graph sampling methods and give an insight to the reason why and how they
revise SRW. our summary includes classical methods and state-of-art RW-based
methods. There are 3 ways to propose new algorithms based on SRW, including SRW
and its combinations, modified selection mechanisms, and the graph topology
modification. We explained the ideas behind those algorithms, and present
detailed pseudo codes. In addition, we add the mathematics behind random walk,
and the essence of random walk variants, which is not mentioned in detail in
many research papers and literature reviews. Apart from RW-based methods, SRW
also has related with the non-RW and non-TBS methods, we discuss the
relationships between SRW and non-RW methods, and the relationships between SRW
and non-TBS methods. The relations between these approaches are formally argued
and a general framework to bridge theoretical analysis and practical
implementation is provided.
