Sampling algorithms for weighted networks

Many of the real-world networks, such as complex social networks, are intrinsically weighted networks, and therefore, traditional network models, such as binary network models, will result in losing much of the information contained in the edge weights of the networks and is not very realistic. In this paper, we propose that when the network model is chosen to be a weighted network, then the network measures such as degree centrality, clustering coefficient and eigenvector centrality must be redefined and new network sampling algorithms must be designed to take the weights of the edges of the network into consideration. In this paper, first, some network measures for weighted networks are presented and then, six network sampling algorithms are proposed for sampling weighted networks. The evaluation is done through simulations on real and synthetic weighted networks in terms of relative error, skew divergence, Pearson’s correlation coefficient and the Kolmogorov–Smirnov statistic. A number of experiments have been conducted to compare the sampling algorithms for weighted networks proposed in this paper with their counterparts for unweighted networks. The experiments show that existing sampling algorithms for unweighted networks will not produce good results as used for sampling weighted networks when compared to the algorithms proposed in this paper.