Sampling in weighted social networks using a levy flight-based learning automata

Recently, there has been growing interest in social network analysis. Graph models for social network analysis are usually assumed to be a deterministic graph with fixed weights for its edges or nodes. As activities of users in online social networks are changed with time, however, this assumption is too restrictive because of uncertainty, unpredictability and the time-varying nature of such real networks. The existing network measures and network sampling algorithms for complex social networks are designed basically for deterministic binary graphs with fixed weights. This results in loss of much of the information about the behavior of the network contained in its time-varying edge weights of network, such that is not an appropriate measure or sample for unveiling the important natural properties of the original network embedded in the varying edge weights. stochastic graphs, in which weights associated with the edges are random variables, can be a suitable model for complex social network. In this paper, according to the principle that Social networks are one of the cases where the distribution of links to nodes is according to the power law that we proposed Levy's initial flight automation sampling algorithm for random graphs, which is a good model for complex social networks. Using Levy Flight instead of gait-based learning that guarantees part of the solution is not separate from the present solution, therefore, it endores an optimizer tolerance, local optimal tolerance, and early convergence. In order to study the performance of the proposed sampling algorithms, several experiments are conducted on real and synthetic stochastic graphs. These algorithms ‘performance is evaluated based on the relative cost, Kendall correlation coefficient, Kolmogorov–Smirnov D statistics, and relative error.