Jerzy Jaworski

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We study a uniform model for random interval graphs on the unit interval. We derive exact results and limit theorems for the distribution of random variables related to the connectivity of this random interval graph. While having the same threshold function for some properties like the Poisson approximation for the number of isolated vertices, our results(More)
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 for the correlation coefficient of degrees of adjacent nodes (called the assortativity coefficient), the expected number of common neighbours of adjacent nodes, and(More)
Two general random intersection graph models (active and passive) were introduced by Godehardt and Jaworski (Exploratory Data Analysis in Empirical Research, Springer, Berlin, Heidelberg, New York, pp. 68–81, 2002). Recently the models have been shown to have wide real life applications. The two most important ones are: non-metric data analysis and real(More)
In this paper we consider a cutting process for random mappings. Specifically, for 0 < m < n, we consider the initial (uniform) random mapping digraph Gn on n labelled vertices, and we delete (if possible), uniformly and at random, m non-cyclic directed edges from Gn. The maximal random digraph consisting of the uni-cyclic components obtained after cutting(More)