2023/12/23 by Fei Ma, Jinzhi Ouyang, Ma, Fei +7
Physics and Astronomy · Mathematics · #Complex Network Analysis Techniques #Graph theory and applications #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2312.15248
The family of planar graphs is a particularly important family and models many real-world networks. In this paper, we propose a principled framework based on the widely-known Apollonian packing process to generate new planar network, i.e., Type-II Apollonian network At. The manipulation is different from that of the typical Apollonian network, and is proceeded in terms of the iterative addition of triangle instead of vertex. As a consequence, network At turns out to be hamiltonian and eulerian, however, the typical Apollonian network is not. Then, we in-depth study some fundamental structural properties on network At, and verify that network At is sparse like most real-world networks, has scale-free feature and small-world property, and exhibits disassortative mixing structure. Next, we design an effective algorithm for solving the problem of how to enumerate spanning trees on network At, and derive the asymptotic solution of the spanning tree entropy, which suggests that Type-II Apollonian network is more reliable to a random removal of edges than the typical Apollonian network. Additionally, we study trapping problem on network At, and use average trapping time as metric to show that Type-II Apollonian network At has better structure for fast information diffusion than the typical Apollonian network.