  Nearest neighbor search has found numerous applications in machine learning,
data mining and massive data processing systems. The past few years have
witnessed the popularity of the graph-based nearest neighbor search paradigm
because of its superiority over the space-partitioning algorithms. While a lot
of empirical studies demonstrate the efficiency of graph-based algorithms, not
much attention has been paid to a more fundamental question: why graph-based
algorithms work so well in practice? And which data property affects the
efficiency and how? In this paper, we try to answer these questions. Our
insight is that "the probability that the neighbors of a point o tends to be
neighbors in the KNN graph" is a crucial data property for query efficiency.
For a given dataset, such a property can be qualitatively measured by
clustering coefficient of the KNN graph. To show how clustering coefficient
affects the performance, we identify that, instead of the global connectivity,
the local connectivity around some given query q has more direct impact on
recall. Specifically, we observed that high clustering coefficient makes most
of the k nearest neighbors of q sit in a maximum strongly connected component
(SCC) in the graph. From the algorithmic point of view, we show that the search
procedure is actually composed of two phases - the one outside the maximum SCC
and the other one in it, which is different from the widely accepted single or
multiple paths search models. We proved that the commonly used graph-based
search algorithm is guaranteed to traverse the maximum SCC once visiting any
point in it. Our analysis reveals that high clustering coefficient leads to
large size of the maximum SCC, and thus provides good answer quality with the
help of the two-phase search procedure. Extensive empirical results over a
comprehensive collection of datasets validate our findings.
