Soft happy colourings and community structure of networks

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

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