Table 1 List of symbols

p

Center of the hyperbola in the hyperbolic model

p _R

Center of the hyperbola in the graphon hyperbolic model

θ

Boundary of the hyperbola in the hyperbolic model

θ _R

Boundary of the hyperbola in the graphon hyperbolic model

γ

Size of the core in the fixed model

H

Thickness of the tail in the fixed model

γ _R

Relative size of the core in the graphon fixed model

H _R

Relative thickness of the tail in the graphon fixed model

d _in

Density of edges inside the community

d _out

Density of the edges outside the community

\(\mathbb {N}\)

Set of natural numbers {0,1,2,…}