Analysis of Heterogeneous Complex Networks Using the Degree of Diffusion

Abstract

Diffusion is the process of spreading information throughout a network. The degree of diffusion a has been used to measure the diffusion and the adoption rates of different complex networks. It is defined as the percentage between the adopters and non-adopters in a network during the diffusion process. In our previous work [1], we only studied the degree of diffusion for directed networks. In this paper, we extend our previous work by using the degree of diffusion to calculate the adoption rate and applied it on two different directed real networks, Caenorhabditis elegans worm's neural network and Positive sentiment social network, then we compared our results with the results obtained in [1]. In addition, we extended the work by applying the same technique on generated undirected networks: random network, scale-free network, and small-world network. They were also applied on three undirected real networks, dolphin social network, yeast protein-protein network, and US power grid network. The results showed that the degree of diffusion a of undirected networks is different than directed networks. For instance, the average number of degree of diffusion was 148 for directed random network where it was 1.9705 for undirected random network. All the obtained results showed that in real networks, randomization does not exist. The behavior of these networks is determined based on the network's members and the interactions between them. Therefore, most of the real networks should be classified as small-world, scale-free networks, or what we defined as small-world random, small-world scale-free networks.