Valentas Kurauskas

Recent Progress in Complex Network Analysis: Properties of Random Intersection Graphs

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 theoretical random graph models, this tendency is described by the clustering coefficient being bounded away from zero. Complex networks also have power-law degree distributions and short average distances (small world phenomena). These are desirable features of random graphs used for modeling real life networks. We survey recent results concerning various random intersection graph models showing that they have tunable clustering coefficient, a rich class of degree distributions including power-laws, and short average distances.

Clustering function: another view on clustering coefficient

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 clustering properties of the network and extends the global clustering coefficient. Our empirical study shows that the function r → cl(r) exhibits a typical sigmoid pattern. In order to better understand this pattern we establish the large scale asymptotics of cl(·) for two related random intersection graph models of affiliation networks admitting a non-vanishing global clustering coefficient. key words: Clustering coefficient, social network, affiliation network, clustering function, random intersection graph.

On the Chromatic Index of Random Uniform Hypergraphs

Let

On small subgraphs in a random intersection digraph

\mathbb{H}^{(k)}(n, N)

On the genus of the complete tripartite graph K n , n , 1

, where

Clustering coefficient of random intersection graphs with infinite degree variance

k \ge 2

Assortativity and clustering of sparse random intersection graphs

, be a random hypergraph on the vertex set

Random graphs with few disjoint cycles

[n] = \{1, 2, \dots, n\}

Large Cliques in Sparse Random Intersection Graphs

with

Clustering function: a measure of social influence

N