Please wait a minute...
Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

Postal Subscription Code 80-964

2018 Impact Factor: 0.565

Front Math Chin    2012, Vol. 7 Issue (1) : 117-124    https://doi.org/10.1007/s11464-011-0165-2
RESEARCH ARTICLE
Joint probability generating function for degrees of active/passive random intersection graphs
Yilun SHANG()
Institute for Cyber Security, University of Texas at San Antonio, San Antonio, TX 78249, USA
 Download: PDF(128 KB)   HTML
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

Correlations of active and passive random intersection graphs are studied in this paper. We present the joint probability generating function for degrees of Gactive(n, m, p) and Gpassive(n, m, p), which are generated by a random bipartite graph G?(n, m, p) on n + m vertices.

Keywords Random graph      intersection graph      degree      generating function     
Corresponding Author(s): SHANG Yilun,Email:shylmath@hotmail.com   
Issue Date: 01 February 2012
 Cite this article:   
Yilun SHANG. Joint probability generating function for degrees of active/passive random intersection graphs[J]. Front Math Chin, 2012, 7(1): 117-124.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-011-0165-2
https://academic.hep.com.cn/fmc/EN/Y2012/V7/I1/117
1 Eschenauer L, Gilgor V D. A key-management scheme for distributed sensor networks. In: Proc 9th ACM Conference of Computer and Communications Security . 2002, 41-47
doi: 10.1145/586110.586117
2 Feller W. An Introduction to Probability Theory and Its Applications, Vol 1. New York: Wiley, 1968
3 Godehardt E, Jaworski J. Two models of random intersection graphs for classification. In: Schwaiger M, Opitz O, eds. Exploratory Data Analysis in Empirical Research . Berlin: Springer-Verlag, 2003, 67-81
doi: 10.1007/978-3-642-55721-7_8
4 Jaworski J, Karoński M, Stark D. The degree of a typical vertex in generalized random intersection graph models. Discrete Math , 2006, 306: 2152-2165
doi: 10.1016/j.disc.2006.05.013
5 Jaworski J, Stark D. The vertex degree distribution of passive random intersection graph models. Combin Probab Comput , 2008, 17: 549-558
doi: 10.1017/S0963548308009103
6 Karoński M, Scheinerman E R, Singer-Cohen K B. On random intersection graphs: the subgraph problem. Combin Probab Comput , 1999, 8: 131-159
doi: 10.1017/S0963548398003459
7 Newman M E J. The structure of scientific collaboration networks. Proc Natl Acad Sci USA , 2001, 98: 404-409
doi: 10.1073/pnas.021544898
8 Newman M E J. Properties of highly clustered networks. Phys Rev E , 2003, 68: 026121
doi: 10.1103/PhysRevE.68.026121
9 Shang Y. Degree distributions in general random intersection graphs. Electron J Combin , 2010, 17: R23
10 Shang Y. Typical vertex degrees in dense generalized random intersection graphs. Math Appl , 2010, 23: 767-773
11 Shang Y. Groupies in random bipartite graphs. Appl Anal Discrete Math , 2010, 4: 278-283
doi: 10.2298/AADM100605021S
12 Shang Y. On the isolated vertices and connectivity in random intersection graphs. Int J Comb , 2011, 2011: 872703
13 Singer-Cohen K B. Random Intersection Graphs. Dissertation . Baltimore: Johns Hopkins University, 1995
14 Stark D. The vertex degree distribution of random intersection graphs. Random Structures Algorithms , 2004, 24: 249-258
doi: 10.1002/rsa.20005
[1] Dongmei CHEN, Zhibing CHEN, Xiao-Dong ZHANG. Spectral radius of uniform hypergraphs and degree sequences[J]. Front. Math. China, 2017, 12(6): 1279-1288.
[2] Ziwen HUANG,Xiangwen LI. Degree sum of a pair of independent edges and Z3-connectivity[J]. Front. Math. China, 2016, 11(6): 1533-1567.
[3] Kinkar Ch. DAS,Sumana DAS,Bo ZHOU. Sum-connectivity index of a graph[J]. Front. Math. China, 2016, 11(1): 47-54.
[4] Kinkar Ch. DAS,Kexiang XU,Junki NAM. Zagreb indices of graphs[J]. Front. Math. China, 2015, 10(3): 567-582.
[5] B. AKBARI,A. R. MOGHADDAMFAR. OD-Characterization of certain four dimensional linear groups with related results concerning degree patterns[J]. Front. Math. China, 2015, 10(1): 1-31.
[6] Yunshu GAO,Qingsong ZOU. Disjoint K4- in claw-free graphs with minimum degree at least five[J]. Front. Math. China, 2015, 10(1): 53-68.
[7] Jinshan XIE, An CHANG. H-Eigenvalues of signless Laplacian tensor for an even uniform hypergraph[J]. Front Math Chin, 2013, 8(1): 107-127.
[8] A. A. HOSEINI, A. R. MOGHADDAMFAR, . Recognizing alternating groups A p +3 for certain primes p by their orders and degree patterns[J]. Front. Math. China, 2010, 5(3): 541-553.
[9] A. R. MOGHADDAMFAR, A. R. ZOKAYI, . OD-Characterization of alternating and symmetric groups of degrees 16 and 22[J]. Front. Math. China, 2009, 4(4): 669-680.
[10] WANG Tao, YU Qinglin. On vertex-coloring 13-edge-weighting[J]. Front. Math. China, 2008, 3(4): 581-587.
[11] ZHANG Liangcai, SHI Wujie. OD-Characterization of all simple groups whose orders are less than 10[J]. Front. Math. China, 2008, 3(3): 461-474.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed