Similarity assessment is one of the core tasks in hyperlink
analysis. Recently, with the proliferation of applications,
e.g., web search and collaborative filtering, SimRank has
been a well-studied measure of similarity between two nodes
in a graph. It recursively follows the philosophy that “two
nodes are similar if they are referenced (have incoming edges)
from similar nodes”, which can be viewed as an aggregation
of similarities based on incoming paths. Despite its popularity,
SimRank has an undesirable property, i.e., “zerosimilarity”:
It only accommodates paths with equal length
from a common “center” node. Thus, a large portion of
other paths are fully ignored. This paper attempts to remedy
this issue. (1) We propose and rigorously justify SimRank*,
a revised version of SimRank, which resolves such
counter-intuitive “zero-similarity” issues while inheriting merits
of the basic SimRank philosophy. (2) We show that
the series form of SimRank* can be reduced to a fairly
succinct and elegant closed form, which looks even simpler
than SimRank, yet enriches semantics without suffering
from increased computational cost. This leads to a fixedpoint
iterative paradigm of SimRank* in O(Knm) time on
a graph of n nodes and m edges for K iterations, which is
comparable to SimRank. (3) To further optimize SimRank*
computation, we leverage a novel clustering strategy via
edge concentration. Due to its NP-hardness, we devise an ef-
ficient and effective heuristic to speed up SimRank* computation
to O(Knm˜ ) time, where ˜m is generally much smaller
than m. (4) Using real and synthetic data, we empirically
verify the rich semantics of SimRank*, and demonstrate its
high computation efficiency.