  We study the statistical properties of the sampled networks by a random
walker. We compare topological properties of the sampled networks such as
degree distribution, degree-degree correlation, and clustering coefficient with
those of the original networks. From the numerical results, we find that most
of topological properties of the sampled networks are almost the same as those
of the original networks for $\gamma \lesssim 3$. In contrast, we find that the
degree distribution exponent of the sampled networks for $\gamma>3$ somewhat
deviates from that of the original networks when the ratio of the sampled
network size to the original network size becomes smaller. We also apply the
sampling method to various real networks such as collaboration of movie actor,
world wide web, and peer-to-peer networks. All topological properties of the
sampled networks show the essentially same as the original real networks.
