2021/11/02 by Nicolas Lanchier, Lanchier, Nicolas, La Salle, Axel +1
Mathematics · Physics and Astronomy · #60K35 #Complex Network Analysis Techniques #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2111.01982
openalex publication_date 2021/11/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Motivated by network resilience and insurance premiums in the context of\ncyber security, we derive universal upper bounds for the first and second\nmoments of the size of bond percolation clusters on finite regular graphs.\nThinking of the clusters as dynamical objects coupled with branching processes\ngives a first set of bounds that are accurate when the probability of an edge\nbeing open is small. Estimating the number of isolated vertices, we also obtain\na second set of bounds that are accurate when the probability of an edge being\nclosed is small. As an illustration, we apply our results to the first three\nPlatonic solids.\n