A random intersection digraph: Indegree and outdegree distributions

Let S(1),...,S(n),T(1),...,T(n) be random subsets of the set [m]={1,...,m}. We consider the random digraph D on the vertex set [n] defined as follows: the arc i->j is present in D whenever S(i)@?T(j) 0@?. Assuming that the pairs of sets (S(i),T(i)), 1@?i@?n, are independent and identically distributed, we study the in- and outdegree distributions of a typical vertex of D as n,m->~.

[1]  Dudley Stark.  The vertex degree distribution of random intersection graphs , 2004 .

[2]  James Allen Fill,et al.  Random intersection graphs when m= w (n): an equivalence theorem relating the evolution of the G ( n, m, p ) and G ( n,P /italic>) models , 2000 .

[3]  Edward R. Scheinerman,et al.  On Random Intersection Graphs: The Subgraph Problem , 1999, Combinatorics, Probability and Computing.

[4]  Gregory Gutin,et al.  Digraphs - theory, algorithms and applications , 2002 .

[5]  Jerzy Jaworski,et al.  The degree of a typical vertex in generalized random intersection graph models , 2006, Discret. Math..

[6]  Willemien Kets,et al.  RANDOM INTERSECTION GRAPHS WITH TUNABLE DEGREE DISTRIBUTION AND CLUSTERING , 2009, Probability in the Engineering and Informational Sciences.

[7]  Mindaugas Bloznelis.  Degree distribution of a typical vertex in a general random intersection graph , 2008 .

[8]  Christina Zamfirescu,et al.  Connection digraphs and second-order line digraphs , 1982, Discret. Math..

[9]  Stefanie Gerke,et al.  Connectivity of the uniform random intersection graph , 2008, Discret. Math..

[10]  Svante Janson,et al.  Random graphs , 2000, Wiley-Interscience series in discrete mathematics and optimization.

[11]  Erhard Godehardt,et al.  Two Models of Random Intersection Graphs for Classification , 2003 .

[12]  Virgil D. Gligor,et al.  A key-management scheme for distributed sensor networks , 2002, CCS '02.

[13]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[14]  Svante Janson,et al.  Random graphs , 2000, ZOR Methods Model. Oper. Res..

[15]  Maurizio Vichi,et al.  Studies in Classification Data Analysis and knowledge Organization , 2011 .