Assuming that actors u and v have r common neighbors in a social network we are interested in how likely is that u and v are adjacent. This question is addressed by studying the collection of conditional probabilities, denoted cl(r), r = 0, 1, 2, . . . , that two randomly chosen actors of the social network are adjacent, given that they have r common neighbors. The function r → cl(r) describes ...

We consider a configuration graph with N vertices whose degrees are independent and identically distributed according to the power law depending on slowly varying function. Configuration graphs widely used for modeling complex communication networks such as Internet. The parameter of power-law distribution is usually selected so that vertex degree has finite expectation infinite variance. An im...

In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution usually has an infinite variance. Therefore, we are especially interested in such degree distributions. In addition, we analyze the clustering coefficient for ...

We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski (2001). For sparse graphs with positive clustering coefficient, we examine statistical dependence between the (local) clustering coefficient and the degree. Our results are mathematically rigorous. They are consistent...

Since its introduction in the year 1998 by Watts and Strogatz, the clustering coefficient has become a frequently used tool for analyzing graphs. In 2002 the transitivity was proposed by Newman, Watts and Strogatz as an alternative to the clustering coefficient. As many networks considered in complex systems are huge, the efficient computation of such network parameters is crucial. Several algo...