Feature Analysis for Model with Cluster Structure

Cluster structure is an essential graph property, however, there is a lack of models which produce the the cluster structure similar to the real one. The paper considers the model described in the article "Model of community emergence in weighted social networks" (Kumpula et al., 2008). This model characterized the cluster structure, but it was not studied in the details. The analysis of the cluster structure of the generated network was carried out, which showed that the cluster size distribution does not follow the power law, moreover, with partial approximation of the obtained distribution by a power law, the distribution index is $\alpha \approx 3 $, while, according to many researches, for real data holds $\alpha \le 2 $. Moreover, the paper proposes a modification of the initial model, which provide an opportunity to generate a graph with a known average weight of vertices, which can be calculated through the inputs of the model. Besides, it was shown that the number of algorithm iterations chosen by the authors significantly exceeds the number of iterations required for the network to reach the stationary state.