scholarly journals Moment-Based Parameter Estimation in Binomial Random Intersection Graph Models

2017 ◽  
pp. 1-15 ◽  
Author(s):  
Joona Karjalainen ◽  
Lasse Leskelä
Keyword(s):  
Parameter Estimation ◽  
Intersection Graph ◽  
Graph Models ◽  
Random Intersection Graph

The Vertex Degree Distribution of Passive Random Intersection Graph Models

2008 ◽  
Vol 17 (4) ◽  
pp. 549-558 ◽  
Author(s):  
JERZY JAWORSKI ◽  
DUDLEY STARK
Keyword(s):  
Degree Distribution ◽  
Graph Model ◽  
Fixed Number ◽  
Vertex Degree ◽  
Intersection Graph ◽  
Graph Models ◽  
Random Size ◽  
Random Intersection Graph

In a random passive intersection graph model the edges of the graph are decided by taking the union of a fixed number of cliques of random size. We give conditions for a random passive intersection graph model to have a limiting vertex degree distribution, in particular to have a Poisson limiting vertex degree distribution. We give related conditions which, in addition to implying a limiting vertex degree distribution, imply convergence of expectation.

scholarly journals The degree of a typical vertex in generalized random intersection graph models

2006 ◽  
Vol 306 (18) ◽  
pp. 2152-2165 ◽  
Author(s):  
Jerzy Jaworski ◽  
Michał Karoński ◽  
Dudley Stark
Keyword(s):  
Intersection Graph ◽  
Graph Models ◽  
Random Intersection Graph

scholarly journals On the Isolated Vertices and Connectivity in Random Intersection Graphs

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Random Graphs ◽  
Intersection Graph ◽  
Intersection Graphs ◽  
Random Intersection Graph ◽  
Probability Of Connectivity ◽  
Asymptotic Probability

We study isolated vertices and connectivity in the random intersection graph . A Poisson convergence for the number of isolated vertices is determined at the threshold for absence of isolated vertices, which is equivalent to the threshold for connectivity. When and , we give the asymptotic probability of connectivity at the threshold for connectivity. Analogous results are well known in Erdős-Rényi random graphs.

scholarly journals Degree Distribution of an Inhomogeneous Random Intersection Graph

10.37236/2786 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Mindaugas Bloznelis ◽  
Julius Damarackas
Keyword(s):  
Degree Distribution ◽  
Intersection Graph ◽  
Random Intersection Graph

We show the asymptotic degree distribution of the typical vertex of a sparse inhomogeneous random intersection graph.

scholarly journals Component Evolution in Random Intersection Graphs

10.37236/935 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Michael Behrisch
Keyword(s):  
Real World ◽  
Linear Order ◽  
Graph Model ◽  
Vertex Degree ◽  
Intersection Graph ◽  
Giant Component ◽  
Logarithmic Order ◽  
Intersection Graphs ◽  
Similarity Network ◽  
Random Intersection Graph

We study the evolution of the order of the largest component in the random intersection graph model which reflects some clustering properties of real–world networks. We show that for appropriate choice of the parameters random intersection graphs differ from $G_{n,p}$ in that neither the so-called giant component, appearing when the expected vertex degree gets larger than one, has linear order nor is the second largest of logarithmic order. We also describe a test of our result on a protein similarity network.

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