  Google employs PageRank to rank web pages, determining the order in which
search results are presented to users based on their queries. PageRank is
primarily utilized for directed networks, although there are instances where it
is also applied to undirected networks. In this paper, we have applied PageRank
to undirected networks, showing that a vertex's PageRank relies on its initial
value, often referred to as an intrinsic, non-network contribution. We have
analytically proved that when the initial value of vertices is either
proportional to their degrees or set to zero, the PageRank values of the
vertices become directly proportional to their degrees. Simulated and empirical
data are employed to bolster our research findings. Additionally, we have
investigated the impact of initial values on PageRank localization.
