Closure coefficients in scale-free complex networks

The formation of triangles in complex networks is an important network property that has received tremendous attention. The formation of triangles is often studied through the clustering coefficient. The closure coefficient or transitivity is another method to measure triadic closure. This statistic measures clustering from the head node of a triangle (instead of from the center node, as in the often studied clustering coefficient). We perform a first exploratory analysis of the behavior of the local closure coefficient in two random graph models that create simple networks with power-law degrees: the hidden-variable model and the hyperbolic random graph. We show that the closure coefficient behaves significantly different in these simple random graph models than in the previously studied multigraph models. We also relate the closure coefficient of high-degree vertices to the clustering coefficient and the average nearest neighbor degree.