Generating weighted social networks using multigraph

Social networks have attracted increasing attention from both academic and industrial societies recently, and weighted social networks play an important role in the studies of information diffusion and influence maximization. To consider the formation process of weighted social networks, we propose an evolving multigraph model. The degree distribution of the generated network can be analyzed theoretically. We then transfer this multigraph to a weighted simple graph by defining the weight for each link, which is continuous and can be regarded as the propagation probability. We observe that the neighborhood overlap rate between two nodes increases with the link weight, which has already been verified by empirical studies. We also find that the degree distribution of this simple graph shows the power-law form and is very close to that of the multigraph. Besides, this simple graph exhibits positive degree correlation and high clustering. Moreover, we validate the model by comparing the generated weighted network with a real-world social network, and find the properties of the generated weighted network are close to those of the real-world one. These results are of importance to understand the structure of weighted social networks as well as the emergence of link weights, and the model can be easily extended to consider more realistic situations.