We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions forâ€¦ (More)

The classical ErdÅ‘s-PÃ³sa theorem states that for each positive integer k there is an f(k) such that, in each graph G which does not have k + 1 disjoint cycles, there is a blocker of size at mostâ€¦ (More)

An intersection graph defines an adjacency relation between subsets S1, . . . , Sn of a finite set W = {w1, . . . , wm}: the subsets Si and Sj are adjacent if they intersect. Assuming that theâ€¦ (More)

The ErdÅ‘s-PÃ³sa theorem (1965) states that in each graph G which contains at most k disjoint cycles, there is a â€˜blockingâ€™ set B of at most f(k) vertices such that the graph G âˆ’ B is acyclic.â€¦ (More)

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 ofâ€¦ (More)

A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. Anâ€¦ (More)

Given a set of vertices V and a set of attributes W let each vertex v âˆˆ V include an attribute w âˆˆW into a set Sâˆ’(v) with probability pâˆ’ and let it include w into a set S(v) with probability p+â€¦ (More)

Experimental results show that in large complex networks such as internet or biological networks, there is a tendency to connect elements which have a common neighbor. This tendency in theoreticalâ€¦ (More)

Experimental results show that in large complex networks (such as internet, social or biological networks) there exists a tendency to connect elements which have a common neighbor. In theoreticalâ€¦ (More)