2024/01/07 by Anthony Bonato, Trent G. Marbach, Bonato, Anthony +5 · 1 citation
Computer Science · Physics and Astronomy · #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Opinion Dynamics and Social Influence #Peer-to-Peer Network Technologies
paper · pdf · doi:10.48550/arxiv.2401.03496
openalex publication_date 2024/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new graph parameter called the cooling number, inspired by the spread of influence in networks and its predecessor, the burning number. The cooling number measures the speed of a slow-moving contagion in a graph; the lower the cooling number, the faster the contagion spreads. We provide tight bounds on the cooling number via a graph's order and diameter. Using isoperimetric results, we derive the cooling number of Cartesian grids. The cooling number is studied in graphs generated by the Iterated Local Transitivity model for social networks. We conclude with open problems.