Closure coefficients in scale-free complex networks

The formation of triangles in complex networks is an important network property that has received tremendous attention. Recently, a new method to measure triadic closure was introduced: the closure coefficient. 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 analyze 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 multigraph models where its behavior was studied before. We also show that the closure coefficient can be related to the clustering coefficient and the average nearest neighbor degree.