Global Clustering Coefficient in Scale-Free Networks

Clustering coefficient of random intersection graphs with infinite degree variance

“…In what follows we discuss the relation between the result of [17] and our Theorems 1, 2, 3 in some detail. To this aim we briefly recall the argument of [17].…”

“…One motivation of our study was the recent paper [17], which claims that "if the degree distribution obeys the power law with an infinite variance, then the global clustering coefficient tends to zero with high probability as the size of a graph grows." This may look a bit confusing in view of the fact that some large social networks with quite substantial global clustering coefficients are believed to have a power law degree distribution with an infinite variance.…”

“…To this aim we briefly recall the argument of [17]. We call a path x ∼ y ∼ z a cherry produced by vertex y.…”

“…Ostroumova and Samosvat [17] observed that cherries produced by vertices of large degrees highly outnumber the triangles of the graph. Indeed, among the iid degrees d 1 , .…”

“…In this way our theoretical findings contribute to the discussion about whether and when a power law network model with an infinite degree variance can have a non-vanishing global clustering coefficient, cf. [17], where a negative result was obtained. The paper is organized as follows.…”