Measuring diversity of network models using distorted information diffusion process

In this paper, we propose a distorted information diffusion protocol to detect diversity of different network models. The protocol is inspired by the fact that, in real social networks, the information diffusion get influenced by the property of nodes and conduct of the links. Thus, information get deformed/distorted during diffusion process and true amount of information from a spreader never reach to all the nodes in the network. We consider a single spreader which has maximum degree in the network. We divide the entire network in to different layers where the nodes in a layer are defined by the nodes having a fixed distance from the spreader. We observe that the amount of information available at every node in a layer after the diffusion process reaches to saturation, is not equal. Thus, we define density of information profile of a layer that measures the density of information available in a layer. Finally, we define a vector, which we call information diversity vector whose components are density of information of the layers. The dimension of the diversity vector is the number of layers in the entire network. We implement the protocol in standard network models which include Albert-Barabasi preferential attachment Model (ABM), Hierarchical network generation Model (HM), and Watts-Strogatz Model (WSM). We also simulate the protocol in real world networks which include ego-Facebook Network, Collaboration network of ArXiv General Relativity, and Collaboration network of ArXiv High Energy Physics Theory. The simulated results show that the information diversity vectors of ABM and HM is far from reflecting the same in real world networks. However, diversity vector of WSM is similar to that of real world networks which we consider in this paper.