Spectral approach for diffusion phenomena among networked agents

Study on probabilistic diffusion among networked agent is gathering attentions because it can represent information diffusion phenomena in this well-interconnected society that have been led by the development of the internet. In real world networks, modular structure is known as ubiquitous characteristics. And, in this paper, spectral properties of several networks, including modular networks, are precisely investigated and the influences from the spectral properties to the diffusion dynamics among the networked agents are discussed. Then we found that, although dynamics on networks have been often approximated utilizing only the largest eigenvalue of the adjacency matrix in the previous literatures, not only the largest eigenvalue but also the other eigenvalues need to be considered especially in the analysis of modular networks, which is verified by the comparisons between analytical results and numerical simulation results.