  In this paper, we propose a novel statistic of networks, the normalized
clustering coefficient, which is a modified version of the clustering
coefficient that is robust to network size, network density and degree
heterogeneity under different network generative models. In particular, under
the degree corrected block model (DCBM), the "in-out-ratio" could be inferred
from the normalized clustering coefficient. Asymptotic properties of the
proposed indicator are studied under three popular network generative models.
The normalized clustering coefficient can also be used for networks clustering,
network sampling as well as dynamic network analysis. Simulations and real data
analysis are carried out to demonstrate these applications.
