Biased random walk sampling on assortative networks

We study the statistical properties of sampled networks by using a biased random walker on assortative networks. In the biased random walk sampling, all the nodes visited by the biased random walker and the links that connect any pair of visited nodes are sampled. Here, the probability that a walker moves to one of its nearest neighbor depends on the degrees of the nearest neighbors. We compare the topological properties, such as the degree distribution, the degree-degree correlation, and the clustering coefficient of the sampled networks with those of the original networks. From the numerical results, we find that most of the topological properties of the sampled networks by the biased random walk are almost the same as those of the original networks when the network is assortative. Moreover, from the measurement of the clustering coefficient, we find that the hierarchical structures are better inherited through a biased random walk sampling when the network is highly assortative.