2012/09/29 by Zhongzhi Zhang, Bin Wu, Zhang, Zhongzhi +3
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #Complex Network Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #cs.DM #math.CO
paper · pdf · doi:10.48550/arxiv.1210.0090
Manuscript accepted for publication (Discrete Applied Mathematics)
openalex publication_date 2012/09/29 · arxiv created 2014/01/20 · arxiv updated 2014/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we find an exact analytical expression for the number of spanning trees in Apollonian networks. This parameter can be related to significant topological and dynamic properties of the networks, including percolation, epidemic spreading, synchronization, and random walks. As Apollonian networks constitute an interesting family of maximal planar graphs which are simultaneously small-world, scale-free, Euclidean and space filling and highly clustered, the study of their spanning trees is of particular relevance. Our results allow also the calculation of the spanning tree entropy of Apollonian networks, which then we compare with those of other graphs with the same average degree.