Random-walk based sampling is widely used to characterize large graphs by producing samples in the form of nodes. However, existing random-walk based sampling methods only focus on the estimation accuracy of structural properties but suffer from repetitive samples which have adverse effects on obtaining accurate information about the structures over social networks represented by large graphs. Furthermore, these existing methods mainly characterize individual attributes while ignoring the social attributes of the nodes. In this paper, a new random-walk based method, called 2-hop neighbors based random walk or 2-Hopper, is proposed to obtain accurate estimations of both basic and social attributes with fewer repetitive samples. Specifically, 2-Hopper is able to greatly reduce redundant paths among nodes during the sampling process and thus produces few repeats. Based on 2-Hopper's sampling process, a re-weighted estimator is proposed to accurately obtain both the individual and social properties while the latter is obtained by a newly proposed algorithm. Experimental results driven by real-world datasets show that on average 2-Hopper can reduce 4.5 times repetitive samples of the state-of-the-art random-walk based methods and obtain more accurate information about the individual and social attributes while 2-Hopper is able to estimate the structural properties of these attributes accurately over large graphs.INDEX TERMS Random-walk based sampling, few repeats, accurate estimations, basic and social attributes of social networks.