Soft happy colourings and community structure of networks

Mohammad H. Shekarriz, Dhananjay Thiruvady, Asef Nazari +1

For $0<\ddot{I}\le 1$, a $\ddot{I}$-happy vertex $v$ in a coloured graph $G$ has at least $\ddot{I}\cdot \mathrm{deg}(v)$ same-colour neighbours, and a $\ddot{I}$-happy colouring (aka soft happy colourin…