Soft happy colourings and community structure of networks

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Mohammad Hadi Shekarriz, Dhananjay R. Thiruvady, Asef Nazari, Rhyd Lewis

Published: 2025, Last Modified: 04 Nov 2025Comput. Oper. Res. 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Highlights•Soft happy colouring of a graph is related to its community structure.•The colouring used communities can make all the vertices ρ-happy if ρ is small.•The threshold ξ is found so that communities make all the vertices ρ-happy.•Communities of large graphs almost certainly induce ρ-happy colouring.•The heuristic algorithm LMC’s output highly correlates with community structure.